I'm not sure if the Barbary Pirates would count as a terrorist organization but Jefferson sent the Marines to defeat them in North Africa.

The most notable example I can think of is President Grant having to deal with the Ku Klux Klan. The Klan started out as an organization that waged a campaign of violent terror against blacks and white Republicans in the South, especially in South Carolina. The federal government was actually pretty slow to react at first, with military units having orders to not interfere in affairs which were considered to be matters of the state/civilian governments. The Klan also outnumbered the federal forces in South Carolina, particularly in the Upstate. In some areas the Klan could gather a force of ~1000 men in only a few hours.

After South Carolina Republicans lobbied the federal government enough, the Enforcement Act of 1871 aka the Ku Klux Klan Act was passed. The Act allowed for the suspension of habeas corpus and hundreds of members of the Klan were arrested or fined.

However, some of the Klan leaders in South Carolina had gotten word of what was happening and fled the state; one even went to Canada. The Klan had also cut back on many of its activities prior to the arrival of federal troops with the enforcement act, so that past actions could not be prosecuted under the new act. While many members of the Klan were arrested, many were let go without punishment or simply fined. The judicial infrastructure could just not handle that many arrests or court cases. Very few Klan members went to trial and were found guilty.

While some historians believe that the Enforcement Act completely destroyed the Klan, others disagree. One of those is Richard Zuczek in State of Rebellion: Reconstruction in South Carolina. Zuczek uses primary sources from those in charge of prosecuting the Klan in South Carolina to show that the Klan was not destroyed. He uses one contemporary quote that states the prosecutions "were largely a matter of sweeping dirt under the rug."

So according to Zuczek, the Enforcement Acts may have curtailed Klan violence for a brief time but in the long run it actually emboldened Carolina whites hellbent on white supremacy. Many members of the Klan would also be apart of white leagues/rifle organizations/"social" clubs such as Ben Tillman and the Redshirts. These groups violently drove out the Republican government in 1876-1877

edit: I personally agree with Zuczek but that may be due to a recency bias since I just finished up his book. He argues that violent white resistance to Reconstruction was commonplace and a continuation of the Civil War.

You really don't begin to see a coherent counter-terrorism policy in the U.S. until the Nixon administration, but even then the policy was fairly limited. Kissinger himself said that the administration never really gave much importance to terrorism at a time when airplane hijackings, particularly by Palestinian nationalist groups, were on the rise.

The first really comprehensive counter-terrorism policy didn't arrive until early in Ronald Reagan's second term. From my own research, I think by far the most significant aspect of counter-terrorism policy from Reagan all the way to George W. Bush is that, despite a drastic increase in the number and severity of terrorist attacks, the various administrations never really focused primarily on the terrorist groups themselves; instead, they focused on state-sponsors of terrorism. In other words, these administrations were never really able to accept the increasingly influential role that non-state actors played on the world stage. Because of that, they attempted to make sense of international terrorism through the only framework that they understood--namely, through state-to-state relations. We see this with Reagan's idea of an "International Murder, Inc." that was made up of various third-world state sponsors of terrorism like Iraq, Iran, Libya, and Nicaragua. Clinton continued Reagan's focus on states over terrorist groups themselves, only changing the rhetoric. Instead of Murder, Inc. we got "rogue states." The trend continues all the way through George W. Bush with his "axis of evil."

This isn't to say that these administrations did not have any plans for dealing with violent non-state actors. They certainly did. But I think the important thing to recognize is that these policies were only meant to supplement the (supposedly) much more important issue of tackling state-sponsors of terrorism, the assumption being that if you stop the sponsorship then you stop the terrorism. I would argue that it is only during the Obama administration that you really begin to see the U.S. give due credence to terrorist groups themselves. This certainly doesn't imply that Obama's counter-terrorism policy is right or effective, but we have finally taken a step in the right direction toward understanding the influence non-state actors can hold in the contemporary world order.

The only other time that I can think of where we have seen a similar recognition by the U.S. of the influence of violent non-state actors is in the late 19th and early 20th century, as European states and the U.S. created forms of international policing that attempted to deal with the transnational wave of anarchist terrorism. Unfortunately, I'm not quite as well-versed in this era although it's a topic I'm currently trying to learn more about.

Edit: I will briefly add something regarding anarchist terrorism. In general, after Europe and the U.S. stepped up international and domestic policing programs, we see the collapse of many anarchist groups, at times through oppressive measures. The significance of this lies primarily in how these policing efforts were integral to state-building within these countries. In attempting to stop anarchist terrorism, states were drastically able to expand powers over their citizens and held a great deal of influence in shaping the modern Western state.

If I could pose a related a related question: To what degree was terrorism an issue in earlier US occupations with prominent insurgencies, such as the Philippines or during the Indian Wars?

Good People, what about the biggest fear and response to "terrorism" in 19th century American history? The fear of black slave insurrection and white enablers. Bloody Kansas, John Brown, Gabriel Prosser (which at least politically was important in 1800), Nat Turner, Charles Deslondes and the Georgia Coast Uprising, etc.

I don't feel like i know enough to go into detail on Presidential responses to these sorts of acts (except to note they help explain Tyler's hostile reaction to the Armistad rebel slaves) but they do prompt political action and fear of this sort of terrorism influences say freedom to disseminate information via the postal system.

Can someone elaborate on this point or argue that i'm off base here (say due to limits of presidential action)?

[This podcast] (http://backstoryradio.org/shows/fear-tactics-a-history-of-domestic-terrorism/) by three Virginia historians made me think of this angle and it includes an interview with the author of "The Day Wall Street Exploded" which is mentioned in /u/gent2012 comment.