That has not, though, stopped both factions of the party from claiming that they are the ones seeking to assure passage of his agenda.
The result is quite a turnabout.
“We are fighting for the Build Back Better agenda,” said Ms. Omar, employing Mr. Biden’s preferred slogan — which would have been shocking at this time two years ago, when she rallied early to Mr. Sanders’s candidacy.
Throughout 2019 and in the first months of 2020, Mr. Biden was an object of scorn from the left. He was too old, too moderate and an obviously bad fit for an increasingly young, diverse and progressive party, they said, often mocking him in harsh terms.
Mr. Biden believed liberals were the ones out of step with the Democratic center of gravity. And he effectively proved it by assembling a multiracial coalition that was animated by defeating Mr. Trump more than by any bold policy agenda.
Yet because his primary had largely centered on ousting Mr. Trump and unifying the country, he had little in the way of firm policy plans. And in making peace with progressives after he secured the nomination, he adopted a number of their ideas.
That has allowed left-wing Democrats to say, with wide smiles, that they are only trying to fulfill Mr. Biden’s vision. The question now is whether his attempt to pass both bills will pay off — or if his decision to not push for quick passage of the infrastructure bill will leave him with a protracted standoff, or nothing at all.
What’s certain, however, is that after Mr. Biden’s all-things-to-all-people campaign, he has committed himself to many of the policies that his liberal critics were skeptical he would embrace.
“For all of the progressives who kept telling me there was no difference between Joe Biden and Mike Bloomberg,” said Representative Brendan Boyle, an early Biden supporter from Philadelphia, “where Biden has come down in this internal debate shows how absurd that claim always was.”