A civil war does not need to be declared. Even normal wars don't really need a formal declaration, with declarations of war usually being a legal process that grants the Chief Executive and the Armed Forces special facultires they don't have during peacetime, but since these faculties are granted by the Legislative power, they can also grant them through ordinary laws. Case in point: the US has not declared war on any country since WWII, and although numerous conflicts are considered wars (Korean, Vietnam, Gulf) they were authorized through Congressional resolutions rather than formal declarations of war.

The Civil War is similar in that there was no need to declare war on the Confederate States. In fact, passing a formal declaration of war would be irrational and defeat the whole position of the upcoming Lincoln administration, because it would recognize the Confederacy as an actual nation on which the US could declare war. Legally, the Confederacy was considered to be a domestic insurrection, and the government does not need to pass legislation to suppress a rebellion. The Lincoln administration never deviated from the position that the Union was intact, the states were still part of it, and that this was a rebellion of individuals that had hijacked legitimate government within the Southern states.

The Insurrection Act of 1807 allowed the President to send the Armed forces into a state for the enforcement of the law if an insurrection took place. This act replaced the Calling Forth Act of 1792, which had a similar goal of allowing the President to use armed forces to suppress rebellion, but only allowed to use the militia. The 1807 Act permitted him to use the Regular Army instead. However, and this is important, the act only allowed the President to use the Army if a state required it. That's why Andrew Jackson used the Insurrection Act to send troops to Virginia after the state requested Federal assiatance to deal with Nat Turner's rebellion, but he couldn't use the act to send forces to South Carolina during the Nullification crisis. Instead, the Congress passed a brand new Force Bill which authorized Jackson to use troops against the will of the South Carolinians.

The Insurrection Act was almost invoked by President John Tyler during Rhode Island's Dorr Rebellion in 1842. Dorr and his supporters, in opposition to the state government which had kept the English Royal Charter, had mounted a completely new rival government that even appointed judges, selected other public offices and created a small armed force to seize the arsenal. Tyler at first did not want to interfere, claiming that the Federal government had no power to intervene in the states with the military. This was incorrect, since the Rhode Island government had requested him to, which meant that Tyler did have the power under the Insurrection Act. Tyler finally decided to intervene after reports arrived that Dorr intended to attack, sending the Secretary of War with authority to federalize the militia and even move Regular troops into the state. In actuality Dorr's force was pretty small, and it dispersed in the face of a larger force raised by the elected governor, so it was not necessary to invoke the Insurrection Act.

But the question of which one was the legitimate government of Rhode Island continued, with the Supreme Court judicial case Luther v. Borden, in which Martin Luther, a supporter of Dorr, was arrested by militia man Luther M. Borden, who allegedly damaged Luther's property. Luther argued that Borden had no authority to do this, since the Rhode Island government was illegitimate. He based this on a clause of the US constitution that requires the Federal government to guarantee a "republican form of government" to every state, and in this case, Luther argued, Rhode Island did not have a republican government since it was based on the aristocratic colonial charter. If the Court found in favor of Luther, it meant that the Dorr government was legitimate; otherwise, it was the elected government. The Court decided that the authority to decide which one was legitimate rested with Congress, which had delegated the power to the President through the Insurrection Act since the President would have to decide which government was legitimate before heeding its call for troops to suppress an insurrection. Tyler's Secretary of War had the authority to call troops against Dorr, so Tyler had, in effect, recognized the elected government. Whether a state government was legitimate or not, the Court concluded, was a political question the President, with authority delegated from Congress, decided.

The importance of these events was to be tested in the actual Civil War. Buchanan came to the feeble conclusion that rebellion was unconstitutional but that the government intervening to put it down was also unconstitutional. Certainly, the Constitution authorizes the Congress to call forth "the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions", but as in other Constitutional articles the devil was in the details. Since the Insurrection Act authorized the use of force only if a state government requested it, then Buchanan could not call the Army unless the very states in rebellion asked him to put the rebellion down! Furthermore, there's the issue that 19th Century Americans put a sometimes fastidious emphasis on the differences between a state and the people of the state, a theme that would continue through the Civil War and Reconstruction. Viewed under the lenses of states rights, the Constitution authorized the government to subdue rebellions of individuals within the states, but not subdue the states themselves. Consequently Buchanan concluded that the Constitution granted him no power "to coerce a State into submission which is attempting to withdraw."

This constitutional debate is part of the reason why Lincoln always insisted that the Civil War was a rebellion of individuals rather than a rebellion of states, and why he rejected Radical doctrines such as Charles Sumner's "state suicide" or Thaddeus Stevens' "conquered provinces." The Congress itself would settle on the doctrine that the "guarantee a republican form of government" clause allowed them to create loyal governments in the Southern states. But I'm getting ahead of myself. When Lincoln assumed the Presidency he had delicate political questions to consider. He, of course, considered secession to be completely unconstitutional and that the President had both the duty and power to stop it. But the Upper South states such as Virginia would secede if he "coerced" the Lower South. But to allow secession to go unmolested would weaken his government and would probably ultimately result in it being irreversible. At this point it was clear that the country was dealing with a political crisis, but there was no armed conflict and thus no Civil War yet.

When the South attacked Fort Sumter, Lincoln decided to call for 75,000 volunteers to put down a rebellion "too powerful to be suppressed by the ordinary course of judicial proceedings". Lincoln used the Militia Act of 1795, not the Insurrection Act (that is why he called for 75,000 three-month volunteers, which was the maximum the act provided. Since the US had been at peace, nobody bothered to update the law). He, again, could not invoke the Insurrection Act because it required the state government to ask him to intervene. Lincoln's legal justification was that it was his duty to enforce the law within the states. Technically, he was not coercing the states but simply enforcing the law against disloyal citizens. As Potter says, "in 1864 a Sherman could devastate Georgia without ever once coercing it" and it would be perfectly constitutional.

Lincoln's call for volunteers, insofar as it transformed the political crisis into an armed conflict, could be considered the "declaration" of Civil War, because in issuing it Lincoln well knew that the Confederacy would interpret it as coercion and would resist accordingly. There is actually some debate over whether Lincoln intended to start a war, was willing to start a war, or started it accidentally when he decided to hold Fort Sumter, but after the bombardment there was no going back. The attack on Fort Sumter could be considered a declaration of war by the Confederacy on the Union, because through it the South said that they would attack the Union unless it recognized its independency. The call for volunteers could be considered a declaration of war by the Union against the Confederacy because it was saying that it would suppress the rebellion, and that entailed the surrender and dismantlement of the Confederacy. But neither actually issued a formal declaration of war - the Confederate position was that it was simply defending its territorial integrity against a foreign presence, while the Union position was that it was suppressing a domestic insurrection by disloyal persons and putting loyal governments in charge.