WASHINGTON — One by one, the Democratic lawmakers stepped to the microphone on Friday, holding on to their letters and an impossible dream: denying the presidency to Donald J. Trump, two weeks before his inauguration.

And one by one, Vice President Joseph R. Biden Jr. — presiding over a joint session of Congress to validate the Electoral College results in Mr. Trump’s victory — turned back their challenges with a stoic message, pounding his gavel without hesitation.

“It is over,” Mr. Biden said at one point, as Republicans rose to their feet to cheer.

After weeks of fitful grumblings about the long-shot maneuvers that might obstruct Mr. Trump’s path to the White House, the proceedings on Friday appeared to close the book.

Lawmakers are permitted to make objections to both individual and state tallies, but they must be submitted in writing and signed by at least one member of both the House and the Senate. No senator chose to join the cause of the half-dozen or so House Democrats who raised complaints.