Representative Josh Gottheimer, a prominent liberal, conceded that the vote is likely to take place “early next week”.
And House Speaker Nancy Pelosi admitted she would not bring the measure to a vote, knowing it would fail.
So far they have been unable to strike a deal between progressive and moderate Democrats on a top figure to structure the programs contained in the bill or plan.
House progressives have said they will not vote for a separate infrastructure package unless it is accompanied by a huge social bill, which the administration has dubbed a “build back better” plan.
“The speaker is an incredibly good vote counter, and she knows where her caucus stands and we’re really clear on that,” Jayapal told CNN’s Jake Tapper when asked about the planned vote on Monday. “The votes are not there. I don’t think she’s going to bring it up.”
Last month, Pelosi committed to passing an infrastructure package by September 27, hoping to placate moderates in support of the big budget blueprint.
Gottheimer, who co-chairs the Problem Solving Caucus, told Tapper that the House would bring the infrastructure bill to the floor for consideration by Monday’s deadline, but that it would not vote until Tuesday at the earliest.
“The way these things work if you start debating this and it rolls by Tuesday, I don’t think — I think we are all reasonable people,” Gotheimer said.
Pelosi also suggested that Monday’s deadline is slipping.
“You can’t choose the date. You have to go when you have the votes at an appropriate time, and we will,” he said, adding that the vote “could happen” on Monday.
“I just want to say that we are going to pass the bill this week,” she said.
Pelosi said it was “self-evident” that the final bill would be smaller than $3.5 trillion.
“Obviously with the talks some changes have to be made to that, and the sooner the better,” she said. “We will do that. This is what the American people need to happen.”
This story and title have been updated with additional developments from Sunday.