The call significantly increases the pressure on Biden, who suffered a disastrous defeat in a debate with Trump last week and is spreading panic among his supporters about his ability to win the November election and hang on to another four years in the White House.
But Biden and his team have so far denied any suggestion he is dropping out of the race.
In response to Doggett's comments, a Biden campaign official told NBC News, “He will remain in his position.”
That and other post-debate assurances from Biden and his campaign have done little to assuage growing concerns among Democrats, some of which are already boiling over in public.
“I think the question that's fair to ask is, is this a seizure or is this a symptom?” former House Speaker and current Rep. Nancy Pelosi, D-Calif., said on MSNBC on Tuesday.
She encouraged Biden to hold multiple in-person interviews with “serious journalists” to reassure allies. Biden has participated in fewer press conferences and interviews than many other contemporary politicians.
Doggett, meanwhile, explicitly tied his decision about Biden to the president's performance in Thursday's debate.
“President Biden continues to lag well behind Democratic senators in key states and also behind President Donald Trump in most polls,” Doggett said in a press release.
“I had hoped that this debate would be a catalyst for change, but it hasn't happened.”
“Instead of reassuring voters, the President has failed to effectively defend many of his accomplishments and expose Mr. Trump's many lies,” the lawmakers said.
“Our first priority must be considering who has the best hope of saving our democracy from a tyrannical takeover by a criminal and his allies,” Doggett said in a statement. “The risks are too great to jeopardize a Trump victory, and too great to think we can overturn now what we couldn't overturn in a year, what we couldn't overturn in the debates.”
“President Biden saved us from President Trump in 2020 and saved our democracy. We must not hand us over to President Trump in 2024,” Doggett said.
The Texas Democrat also warned of the threat posed by Trump's re-election, pointing to the Supreme Court's decision this week granting former presidents “presumed immunity” for all official conduct.
“With his newfound immunity, Trump could lead America into a long, dark era of authoritarianism, unchecked by either the courts or a compliant Republican Congress,” Doggett's statement said.
He urged Biden to follow the example of former President Lyndon Johnson, who declined to run for a second term.
“Under very different circumstances, [Johnson] “We have made the difficult decision to withdraw, and President Biden should do the same,” Doggett said.
“My decision to publicly express these strong concerns was not made lightly and does not diminish in any way my respect for all that President Biden has accomplished,” he said.
“Unlike President Trump, President Biden's first commitment has always been to our country, not himself, and I expect him to make the painful and difficult decision to withdraw.”