This article from the Federation of American Scientists (FAS), The Burr Conspiracy (n/d accessed 04/06/2017, summarizes Burr's plan this way:
When Vice President Aaron Burr killed Alexander Hamilton in a duel in 1804, he also killed his chance to be president. Wanted for murder in New York, he fled the state and went to Philadelphia. Realizing that he had no future on the east coast, Burr, in a frantic effort to salvage his destroyed political power and heavily in debt, conceived a plan to seek political fortunes beyond the Alleghenies. He first contacted the British Minister, Anthony Merry, living in Philadelphia. He offered Merry his services in any efforts by Great Britain to take control over the western part of the United States. Merry, who hated the United States, wrote his Foreign Ministry that while Burr was notoriously profligate, nevertheless, his ambition and spirit of revenge would be useful to the British government. Merry became a strong supporter of Burr's schemes.In 1805, Burr came up with a plan that involved secession:
Burr was dropped from the presidential ticket by Jefferson and in April 1805 commenced to put his plans into motion. He again approached the British via Minister Merry. He informed Merry that Louisiana was ready to break with the United States and once it did all the western country would follow suit. To be successful, Burr requested that Britain assure his protection, provide him with a half of million dollar loan, and dispatch a British naval squadron to the mouth of the Mississippi River. The British might have entertained Burr's requests but Prime Minister Pitt died and was succeeded by Charles James Fox, a life-long friend of the United States. Fox considered the Merry-Burr discussions indiscreet, dangerous and damnable and recalled Merry to England on June 1, 1806. Having failed to secure British aid in an attempt to separate western states from the United States, Burr then headed west across Pennsylvania. [my emphasis]As the article recounts, Jefferson's Administration charged Burr with treason. Burr walked on the treason charge because the highly partisan and anti-Jefferson Supreme Court Justice John Marshall presided over the trial and found him innocent. Jefferson and his supporters had good reason to think that the Chief Justice had not handled the trial well, to put it mildly.
Confronted with this treasonous attempt at secession, Jefferson charged the perpetrator with treason. That was strong statement of his position, even though the active collusion with Britain rather than just the secession plans themselves were also involved.
During the crisis that unfolded during Aaron Burr's conspiracy (which Jefferson ultimately understood as a plan to separate the western states from the Union), Jefferson consulted [Secretary of State James] Madison about whether the executive had the authority to use regular troops in cases of domestic insurrection. When Madison told Jefferson that he did not, Jefferson drafted a bill "authorizing the emploiment [sic] of the land and naval forces of the US. in cases of insurrection" in all situations where the president is authorized to use militia "to suppress such insurrection, or to cause the laws to be duly executed." [my emphasis]But Jefferson celebrated the fact that the crisis was resolved without a resort to force on the part of the federal government:
At all times, though, Jefferson hoped that local authorities would suppress the plot and counted on the loyalty and republicanism of the inhabitants of the western states. After the plot failed, the lesson Jefferson took from it was that government was strongest when "every man feels himself a part" of it - the message of the first inaugural. It proved, too, "the importance of preserving to the State authorities all that vigor which the Constitution foresaw would be necessary, not only for their own safety, but for that of the whole." The "hand of the people" had "given the mortal blow to a conspiracy which, in other countries, would have called for an appeal to armies." Federal force thus seemed unnecessary in a union of such harmony and affection.Steele stresses how emphatically Jefferson insisted on the necessity and justice of the national government preserving itself in the face of a state in open rebellion and attempting to secede from the Union:
But if the people of Ohio and Kentucky and Louisiana had not come through [in foiling the secession plot], Jefferson was prepared for Burr. In his sixth annual message Jefferson reminded Congress that a benign government directed by the will of the people made "insurrection or enterprise on the public peace or authority" nearly unimaginable. Nevertheless, Jefferson remained unwilling to trust such "moral restraints only" and praised the wisdom of laws that "provided punishments for these crimes when committed." But even this seemed insufficient to deal with such a conspiracy against the Union. Accordingly, Jefferson encouraged Congress to pass laws giving him the power to prevent even the "commission" of such crimes. As much as Jefferson trusted the magnetism of affection and interest to hold the Union together, he nonetheless considered a kind of preemptive suppression of "insurrection" a legitimate function of the national government. [my emphasis]Jefferson's record on secession and the need to preserve the Union with the appropriate means to do so, including military coercion, stand out clearly in the Burr conspiracy incident.