President Biden’s resistance to pressure to end his re-election bid appears to be a strategy aimed at running out the clock, a play to leave his party so little time to come up with another candidate that his opponents stand down.

Every day that Mr. Biden defies pressure to step aside, the prospects, and logistics, of replacing him become more untenable, and riskier. And the potential of weeks of Democratic infighting, as a united Republican Party nominates former President Donald J. Trump, may start to look worse than rallying behind Mr. Biden, no matter the concerns about the 81-year-old president’s health and ability to defeat Mr. Trump.

“It’s a mess,” said James Carville, a consultant who has been among a roster of Democrats pushing for Mr. Biden to step aside and clear the way for a new nominee. “Suppose he gets what he wants. Everybody gets exhausted and just says, ‘It’s too much trouble.’”

Mr. Biden’s efforts to dig in were showing signs of initial success. On Tuesday, some Democratic leaders in Congress expressed support for the president and said it was time to move on. “The urgent need right now is for Democrats to stick together and focus on the danger of Trump and his extremist agenda,” said Representative Diana DeGette of Colorado. “If we do that, we will win.”

The calendar is on Mr. Biden’s side. In the coming days, attention will turn to Mr. Trump, who is expected to name a running mate before his party gathers next week in Milwaukee to nominate him for a second term. Mr. Biden will be somewhat out of the public spotlight, focusing on the behind-the-scenes campaign to keep nervous Democrats in line.

There are 35 days between July 18, when Mr. Trump is set to accept his party’s nomination in Milwaukee, and Aug. 22, when Mr. Biden is set to accept his party’s nomination in Chicago. But the Biden campaign, working with the Democratic National Committee, appears ready to compress the calendar even further.