Arkansas senator Tom Cotton told Fox & Friends that Ms Tanden should just step aside now despite her reported deletion of more than 1,000 tweets criticizing everyone from Republican lawmakers to Michelle Obama.
“The problem with Neera Tanden is not so much her tweets, it’s her radical liberal ideas," Mr Cotton said.
“This is a woman who wants Congress to hold up coronavirus relief for the American people so we can give checks to illegal immigrants."
Ms Tanden, a past Hillary Clinton adviser and head of the Centre for American Progress, still has more than 87,000 tweets her personal profile, which has been updated to read “Director of OMB Nominee".
"There is no chance Neera Tanden will be confirmed. She might as well step aside, or, Joe Biden might as well withdraw her and go back to the drawing board,” Mr Cotton said.
Ms Tanden's nomination has received criticisms from both conservatives and progressives, with former White House chief of staff John Podesta telling Politico she had "drawn a bit more fire from some quarters" but that senators should look beyond her Twitter feed.
Among the tweets deleted after 1 November, first reported by the NY Post, Ms Tanden said she was glad Senate majority leader Mitch McConnell is "fiddling, while the markets burn".
Ms Tandeen will need the votes from Mr McConnell and Republican senators to be confirmed if the GOP retains control of the Senate after the January runoff elections in Georgia.
In a tweet his own following her nomination, Mr Cotton slammed Ms Tanden as “a partisan hack who called Susan Collins ‘the worst’.
"Biden said he wanted to unify the country. But he’s picked a national security team that is weak on China, a DHS nominee who sold visas for powerful political friends, and a partisan hack who called Susan Collins “the worst” for OMB. So much for unity," he said.
Biden said he wanted to unify the country.
But he’s picked a national security team that is weak on China, a DHS nominee who sold visas for powerful political friends, and a partisan hack who called Susan Collins “the worst” for OMB.
So much for unity.
— Tom Cotton (@TomCottonAR) November 30, 2020
Among the nominees that Mr Cotton singled out for criticism on Fox was Mr Biden's pick for Treasury secretary, Janet Yellen.
He said Yellen presided over a low growth, stagnant economy that didn't create jobs and wages for working-class Americans.
"It’s just another example of how Joe Biden is going back to the Obama-Biden era, where we’re going to have more taxes and more regulations, not have a government that stands with and stands beside the American people, but rather one that tries to ride the back of the American people with one-size-fits-all policies coming from Washington,” he said.