A key moderate, Rep. Josh Gottheimer, conceded the vote would likely occur "early next week."
And House Speaker Nancy Pelosi acknowledged she wouldn't bring the measure for a vote knowing it would fail.
So far they have been unable to strike a deal between progressive and moderate Democrats on a topline figure for the bill or a framework of programs contained in the plan.
House progressives have said they will not vote for the separate infrastructure package unless it is accompanied by the much larger social bill, dubbed by the administration as the "Build Back Better" plan.
"The speaker is an incredibly good vote counter, and she knows exactly where her caucus stands and we've been really clear on that," Jayapal told CNN's Jake Tapper when asked about the planned vote on Monday. "The votes aren't there. I don't think she's going to bring it up."
Last month, Pelosi committed to passing the infrastructure package by September 27, hoping to placate moderates who were wavering in support for the larger budget blueprint.
Gottheimer, who co-chairs the Problem Solvers Caucus, told Tapper that the House would bring the infrastructure bill to the floor for consideration by Monday's deadline, but that a vote won't take place until Tuesday at the earliest.
"The way these things work if you start debating it and it rolls over to Tuesday, I don't think — I think we're all reasonable people," Gottheimer said.
Pelosi also suggested the Monday deadline was slipping.
"You cannot choose the date. You have to go when you have the votes at a reasonable time, and we will," she said, holding out that the vote "may" happen Monday.
"Let me just say we're going to pass the bill this week," she said.
Pelosi said it was "self-evident" the final bill would be smaller than $3.5 trillion.
"Obviously with negotiations there will have to be some changes in that, and the sooner the better," she said. "We will do that. The American people need that to happen."
This story and headline have been updated with additional developments Sunday.