Mary-Jo Kline, editor of the Burr papers, says that “The new vice president then gave the oath to senators-elect who presented their credentials. Jefferson 'attended by the Heads of Departments, the Marshal of the District, his officers and other gentlemen,' then entered the chamber. Neither the Senate proceedings nor contemporary newspaper accounts record any remarks made by AB and merely note that he vacated his seat at the head of the chamber for the president. AB sat next to the chief justice on the president's right while Jefferson delivered his inaugural address” (Kline 1:519n2, citing Ann. Cong. 6th Cong., p. 762-3; Washington National Intelligencer, 6 March; Washing Federalist, 7 March; NY City Daily Adveriser, 10, 12 March; NY City Amer. Citizen, 10 March).
Isenberg notes that “the most telling gesture was that of Burr graciously offering his seat to the president-elect” (224).
Burr wrote: “The Mail closed at an earlier hour than I had supposed[;] it affords me the opportunity to add – That we have gone through the Ceremony – The Day was serene and temperate – The Concourse of people immense – all passed off handsomely – great joy but no riot – no accident – The Paper Contains Jefferson's Speech – A.B.'s cannot be published for it was not written[;] it consisted of about three sentences” (AB to Caesar A. Rodney, March 3, 1801, Kline 1:518).
Celebrations took place around the country. (Isenberg lists some at 224.) The Albany Register recorded that toasts were given [in Albany] for the president and vice president. For “Aaron Burr, Vice-President of the United States; his uniform and patriotic exertions in favor of Republicanism eclipsed only by his late disinterested conduct” (James Parton, The Life and Times of Aaron Burr , 294-5).
Focusing more on the image of the three men, Burr biographer Milton Lomask wrote “Most members of the audience in the Senate chamber that day would live long enough to have reason to recall with feeling the tableau that now presented itself: Jefferson seated at the center of the platform, flanked on his right by a man he would one day accuse of treason; on his left by the stubborn jurist who would frustrate all efforts to convict the accused” (Lomask, Aaron Burr , 1:297).
Biographers Herbert Parmet and Marie Hecht focused on the meaning of the day to Burr: “Waiting for the swearing-in and anticipating the Inaugural Address, the new Vice President looked forward to political tranquility. From Philadelphia, one week earlier, he had written to Gallatin concerning the charges in circulation about his conduct during the recent campaign. 'They are now,' he had observed, 'of little consequence & those who had believed them will doubtless blush at their own weakness --,' It was natural, or at least it should have been, that his industry and skill should now be rewarded. His friends were sure that Jefferson could not have won without Burr's work. So was he. There was no reason to suspect, therefore, that the journey to the nation's second highest office would be anything but triumphal” (Parmet & Hecht, Aaron Burr: Portrait of an Ambitious Man , 169).
Indeed, according to Albert Beveridge, John Marshall's biographer: “The proof is overwhelming and decisive that nothing but Burr's refusal to help the Federalists in his own behalf, his rejection of their proposals, and his determination, if chosen, to go in as a Republican untainted by any promises; and, on the other hand, the assurances which Jefferson gave Federalists as to office and the principal Federalist policies – Neutrality, the Finances, and the Navy – only all of these circumstances combined finally made Jefferson president” (Beveridge, The Life of John Marshall , 2: 545-6, citing & quoting James Bayard).
In his contemporary letters and in 1806 testimony he gave in a deposition for a lawsuit filed by Burr against James Cheetham, Bayard recorded the views of the "Federalist managers":
"Burr has acted a miserable paultry [sic] part. The election was in his power, but he was determined to come in as a Democrat ... We have been counteracted in the whole business by letters he has written to this place" (Bayard to Bassett, Feb. 16, 1801, quoted in Beveridge, 546n1). Another Federalist wrote: "Had Burr done anything, for himself, he would, long ere this, have been President" (Cooper to Morris, Feb. 13, 1801, id.) Bayard again:“The means existed of electing Burr, but they required his cooperation. By deceiving one Man (a great blockhead) and tempting two (not incorruptible) he might have secured a majority of the States. He will never have another chance of being President of the U.states and the little use he has made of the one which has occurred gives me a humble opinion of the talents of an unprincipled man” (Kline 1:487). (For the complete story of the lawsuit and the texts of the various testimony taken by those involved in the 1801 electoral tie, see Kline 2:872-6.)
With respect to Burr's position in the party at that time, Henry Adams wrote: "Colonel Burr was the chosen head of Northern democracy, idol of the wards of New York city, and aspirant to the highest offices he could reach by means legal or beyond the law" (Adams, 132).
Typically, Burr is considered “unprincipled” for having allegedly aspired to use illegal OR legal means to attain high office as well as when, on the contrary, he made “little use” of his chance to corrupt and deceive others to attain high office.