So there's two things to note here. First is a technical legal point: the actual case involved a Georgia state law that required state authorization to be lawfully present on Indian lands. This was representative of a series of laws passed by the states designed to gradually evict the Indians. The Worcester in the case was a preacher who had violated that law and been convicted. The Court invalidated the law, saying that state laws did not apply on Indian lands, and that Indians were, in effect, under the protection of the federal government and beyond the reach of state law. Nothing to do with Jackson's Indian Removal Act, per se.

This brings me to my second point, which is a lot broader: the U.S. courts are always going to be limited in their authority because they're totally dependent on the political branches (that is, Congress and the executive) for enforcement. As Hamilton pointed out in Federalist 78, Congress controls the money, and the President controls the military and bureaucracy; the courts have no such intrinsic powers beyond their ability to persuade. If the legislature or executive doesn't want to enforce a decision, often times they'll drag their feet or refuse to enforce it at all. This also happened during segregation and during the run-up to the Civil War. Despite Brown v. Board, which ended school segregation, and Dred Scott, legalizing slavery in the territories, being the law of the land, both decisions were divisive and widely ignored.

The Jackson Administration's policy was decidedly anti-Indian, and so the theoretical protection of the federal government meant little; indeed, Jackson refused to use the power of the federal government to hold Georgia accountable, and the states continued to make anti-Indian laws as though nothing had happened. This shouldn't come as a surprise. After all, Jackson and the Congress had passed the Indian Removal Act only two years before in 1830.

Sources: Federalist 78

Barry Friedman, The Will of the People

Worcester v. Georgia, 31 US 515 (1832).

Ok, so I covered this in a module on Native American history from the Antebellum period to the 1970s just last semester, so while I'm by no mean an expert on the subject matter, this is some university-level insight. I'd still recommend getting someone who has specialised on the subject to give you a more in depth answer.

Broadly speaking, rather than Jackson defying the Supreme Court, its more a case of the President and his Administration allowing the State of Georgia to evict the Cherokee without repercussion. The Trail of Tears (at least in regards to the Cherokee removal) actually occurred in 1838, after Jackson was no longer President.

Firstly, it should be quickly noted that the Supreme Court and Georgian legislature had came to disagreements back in 1832 (6 years before the Cherokee were removed from their lands), over laws Georgia had passed regarding the seizure of Native land. It's a whole topic of another question on it's own, but the summary of it is that by setting out laws in which they could negotiate with the Cherokee for land (or more often, force them off the land), the Supreme Court ruled that Georgia had encroached upon the powers of the US Government, on the grounds that the wording of State's law conflicted with a federal statute on the topic, specifically the Non-Intercourse Act (1802).

In an ideal world, the ruling would have been obeyed, and Georgia would have to defered to the Supreme Court's ruling. One such reason for this was States' Rights. Even though the American Civil War wouldn't spark off until Lincoln's presidency in the 1860s, it was the result of discontent over federal involvement in slavery legislation from as far back as early the 1820s. Adding Indian policy into the mix further fostered discontent, and Georgia may or may not have issued threats of secession (unfortunately I don't have access to a citation for this on hand at the moment. If anyone else can back this up with a source, that'd be welcome).

Because of this tension, enforcement of the federal rules was either dealt with limp wristedly or in some cases outright ignored, for fear of exacerbating the issue. Due to Georgia (and other Southern states with Indian borders) conflating States' Rights involving slavery with that of their Indian policy, Jackson (an anti-abolitionist) was uninterested in trying to force the matter. He believed that the only enforcement that would work would be the deployment of federal troops to defend the Cherokee against militias trying to force the Natives off their lands, and that if he did so, Georgia would have a pretext for secession. Also, Jackson had no love lost for Indians, and believed that if the Cherokee attacked in retaliation, he would have a valid reason to order the US Army to slaughter them.

Later that same year the Sixth Land Lottery (also known as the Cherokee Land Lottery) was ran by Georgia. Its nickname comes from the fact that the lands it was auctioning were Cherokee territory that the state didn't actually have a legal claim to, and under the Supreme Court ruling never would. The Georgian Guard began to nonetheless force Cherokees off their land, and by 1835, had evicted a sizeable percentage to lands west of the Mississippi. Major Ridge, a Cherokee leader who had fought alongside Jackson during the Creek War, believed that unless peaceful resolution was settled, massacres similar to the earlier Creek and Seminole wars would befall the Cherokee. After being told by Jackson that the President would not risk sending federal forces to defend the Cherokee sovereignty, Major Ridge and a small group of other Cherokee signed the Treaty of New Echota, a few days before the new year of 1836. This was ratified in Congress a few months later, and would be used to argue the legal validity of the Trail of Tears, despite Ridge and his faction representing only a minority of the Cherokee nation. Congress was shortly afterwards presented with a petition signed by the a vast percentage of the Cherokee nation asking for the Treaty to be voided, however, this petition was ignored.

Following his election as the new President, Martin Van Buren continued the Cherokee removal and Jackson's Indian policy. To do this, he ordered General Winfield Scott to forcibly move any and all Cherokee who had not yet complied with the Treaty. This would be what is known as the Trail of Tears.

To Conclude: Jackson wasn't punished as he never directly opposed the Supreme Court, he simply didn't put much effort into enforcing their ruling. After 1836, Congress had a legal (if flimsy) pretext under Federal statute to remove all Cherokee from their lands, and Van Buren was the President who actually carried out the removal.

Sources:

Heidler, David S. Indian Removal

Hurtardo, Albert et al. Major Problems in American History

James, Marquis. The Life of Andrew Jackson

Norgren, Jill. The Cherokee Cases

Sturgis, Amy H. The Trail of Tears and Indian Removal

I'm much more comfortable talking about this question from the separation of powers and legal position than the historical question of the political reaction to the fallout. So I'll address the "how" question, but not the "was there a repercussion" part, if that's alright. I think, to understand this question, it's important to understand how the Supreme Court works. This is less a history question and more a legal/civics question, but I'll turn back to the specific case in a moment. Contrary to popular belief, the Supreme Court doesn't just make pronouncements from on high about what the law is. Instead, what they do is deal with specific legal cases between specific parties. In doing so, they often have to interpret the law, which includes statutes, treaties, and the US Constitution. This means they'll make rulings about what the law is that will guide courts in the future. However, they generally only interpret the laws that affect the outcome of the case and, if they start talking about other laws, that's what's called dicta (short for "Obiter Dictum," which means "said in passing). Dicta is not considered an official interpretation of the law even if it's said in a court opinion and is not binding on other Judges nor other people. They'll also issue specific orders to specific parties involved in the case. That's when they'll tell people "do this" or "don't do that" or, in criminal cases, they tell the lower court that they got something wrong and to change the outcome of a case.

Now that we've gotten that out of the way, let's talk about your specific question. Here is the Wikipedia article on the Trail of Tears. I believe the quote you're referring to, in context, is this (I condensed one sentence from a second paragraph into one paragraph:

In the years following the Act, the Cherokee filed several lawsuits regarding conflicts with the state of Georgia. Some of these cases reached the Supreme Court, the most influential being Worcester v. Georgia (1832). Samuel Worcester and other non-Indians were convicted by Georgia law for residing in Cherokee territory in the state of Georgia without a license. Worcester was sentenced to prison for four years and appealed the ruling, arguing that this sentence violated treaties made between Indian nations and the United States federal government by imposing state laws on Cherokee lands. The Court ruled in Worcester's favor, declaring that the Cherokee Nation was subject only to federal law and that the Supremacy Clause barred legislative interference by the state of Georgia. Chief Justice Marshall argued, "The Cherokee nation, then, is a distinct community occupying its own territory in which the laws of Georgia can have no force. The whole intercourse between the United States and this Nation, is, by our constitution and laws, vested in the government of the United States." Andrew Jackson did not listen to the Supreme Court mandate barring Georgia from intruding on Cherokee lands.

Now the short answer to your question can be found in three words: "mandate barring Georgia." I don't think that's technically correct either, but, still, the Supreme Court told Georgia what to do, not the President of the United States. Still, I think there's a lot more to it.

To understand Worcester v. Georgia, you need to understand an earlier case called Johnson v. McIntosh. McIntosh involved two people who bought the same plot of land (technically, they actually didn't, but everyone argued in court that it was the same land so, for purposes of the law, it was the same land). Thomas Johnson bought the land from a Native American tribe directly. William McIntosh bought the land from the United States who had acquired the land some time later. Under property law, if Person A buys the land first and has valid title to it, the latter sale to Person B is invalid. However, the Supreme Court held that Person A did not have valid title because he could not legally buy the land from the Indian tribe. Instead, the Court held that the United States had exclusive power to negotiate to buy land from Indian tribes.

The case is widely seen as a blow to Indian sovereignty because it makes them less than fully sovereign. Indians have the rights to occupy their own land, but they don't have the rights to buy and sell it as they see fit. Instead, the only party they can sell land to is the United States government.

That brings us to Worcester v. Georgia. Samuel Worcester was accused of doing business with a Cherokee tribe without a state license. The Supreme Court held that this law was invalid. The key to this case is the same as McIntosh. The United States has exclusive power to regulate relationships with Native Americans. This means that the state of Georgia can't do that (without permission). Therefore, the Supreme Court ordered that Mr. Worcester be released. This is supposedly where President Andrew Jackson responded about the Supreme Court's ruling. He said that Georgia could not be forced to listen to the Supreme Court. For what it's worth, they did drag their feet a bit, but they ultimately more or less complied and pardoned Mr. Worcester on the condition that he stop doing business with Indian tribes.

As you can see, this case has nothing to do with the Trail of Tears and says nothing about whether the President can remove the Cherokee. So why does everyone say this case held that Indian tribes are sovereign and can't be removed? The answer comes back to that word I mentioned earlier: "dicta." The Supreme Court said a lot of things in the case that weren't 100% necessary to solve the case. In Worcester, the Supreme Court was much friendlier to Indian sovereignty than they had been in McIntosh. It analogized the tribes as nations who had the right to govern their own territory as they saw fit. It discussed the treaties between the United States and the Cherokee, said they were the governing law of the United States on this issue, and said those treaties gave no power of the United States to interfere with Cherokee sovereignty. Basically, although the Cherokee could only sell their land to the United States and could not engage with foreign powers, they had all other rights as a sovereign nation.

Ultimately, the sovereignty of Indian tribes proved to be ephemeral. While the Worcester strongly limited what the state of Georgia could do to the Cherokee, it did not require the United States to honor their treaties. Unfortunately, the power of a sovereign nation to enter into treaties includes the power of that nation to break those treaties. It also included the power to negotiate new, more coercive treaties. In other words, the Supreme Court's decision was not about the Trail of Tears and their ruling did nothing to stop the Federal government from acting.