President Biden’s increasingly emphatic declarations that he will not exit the presidential race are delivering an unmistakable message to potential wayward Democrats: Any criticisms going forward damage the party’s chances against Donald J. Trump.

For days, Mr. Biden has said he will remain his party’s nominee after his poor debate short of an intervention from “the Lord Almighty.” On Monday, he put that assertion into action.

It began with an open letter to congressional Democrats saying he was definitely running. It continued with a defiant call into one of his favorite cable news shows decrying the “elites” trying to shove him out. It included a midday appearance on a private video call with some of his campaign’s top financiers as well as a planned private virtual meeting on Monday evening with a bulwark of his past support: the Congressional Black Caucus.

“I am not going anywhere,” Mr. Biden told the donors.

The moves amounted to a show of defiance that the Biden operation hoped would earn him some deference, as uneasy Democratic lawmakers trickled back to Capitol Hill after a holiday break. At the same time, the Biden team was trying to reframe the pressure campaign to get him to step aside as one hatched by the elite party establishment rather than a genuine reflection of grass-roots voter fears about the 81-year-old commander in chief’s age and acuity.

“I love this fighting Joe Biden,” said Representative Robert Garcia of California, a Democrat and an outspoken Biden supporter. “When he takes a punch, he’s going to come back and punch harder.”

Both in his private and public remarks on Monday, Mr. Biden made clear he holds all the cards when determining his political future. He has won every state in the Democratic primaries and 14 million votes, netting him practically every delegate headed to Chicago next month for the party’s convention.