But the majority of Senate Republicans still remain opposed to the plan.
“What we ought to be doing is focusing on the $900 billion that we’ve already approved and that Secretary Mnuchin helped us negotiate,” Senator John Cornyn of Texas said.
“Instead of taking appropriate credit for those good things, focusing on” the issue of larger checks, he continued, “undermines the very positive impact of what we’ve already done.”
“It’s such a huge number,” said Senator James M. Inhofe of Oklahoma. “I’d have a hard time supporting it.”
A decision by Mr. McConnell to link all of Mr. Trump’s demands together could sink the legislation. Democrats are unlikely to endorse a hasty overhaul of the legal shield currently in place for social media companies, known as Section 230 of the Communications Decency Act, especially measures put forward by Republican senators aimed at confronting what they believe is anticonservative bias.
Mr. Trump has attacked Section 230 for months, arguing without evidence that the law enables websites to censor conservative views. Data shows that conservative personalities and publishers often thrive online. Conservative Republicans have introduced multiple bills tackling the issue in the past two years, although none of them have become law.
While the concerns about Section 230 are bipartisan, it is unlikely that lawmakers could reach an agreement on the issue within the next week. Mr. Trump and his allies have yet to find substantial common ground with Democrats who primarily want changes addressing discriminatory advertising or terrorist content online.
“If Senator McConnell tries loading up the bipartisan House-passed CASH Act with unrelated, partisan provisions that will do absolutely nothing to help struggling families across the country, it will not pass the House and cannot become law,” Mr. Schumer said in a statement. “Any move like this by Sen. McConnell would be a blatant attempt to deprive Americans of a $2,000 survival check.”
Despite the lack of action on a bigger check, the Treasury secretary, Steven Mnuchin, said in a Tweet on Tuesday that the $600 checks could begin arriving in bank accounts as early as Tuesday evening and would continue into next week, while paper checks will start being mailed on Wednesday.