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(CNN) —  

Democratic leaders in the House of Representatives will postpone a vote on a budget caps bill that was potentially on tap for Wednesday, as progressive lawmakers continue to demand higher spending levels than leaders had proposed in the bill.

The intraparty debate exposes the Democrats’ first big policy rift in their new majority.

House Budget Chairman John Yarmuth said the House is no longer set to vote on the bill Wednesday, and he argued the party is just experiencing growing pains, with so many members who have never been in the majority before and have never had to govern.

“I don’t think we’d have the votes if we went to the floor right now,” the Kentucky Democrat said. “It’s not going to come up this week.”

House Majority Leader Steny Hoyer, a Maryland Democrat, also confirmed to CNN that the vote would not be held Wednesday.

Rep. Mark Pocan, a co-chair of the Congressional Progressive Caucus, has largely praised the way Democratic leaders, like Speaker Nancy Pelosi of California, have managed the caucus. But Pocan said this issue was different: “Oddly, we weren’t really heard in a way that we felt we needed to be.”

“I think the lesson learned is be as inclusive as possible, especially with large caucuses,” the Wisconsin Democrat said.

The negotiation is intended to be an opening offer for Democrats in the House as they begin the long budget fight with the Republican-controlled Senate and White House. Disagreements within the Democratic ranks would be a bad start and signal a lack of unity as party leaders are forced to negotiate.

Senate Majority Leader Mitch McConnell announced Tuesday afternoon that he and Pelosi had agreed to start talks at the staff level for a two-year deal to raise the spending caps.

“So I am hoping this will be the beginning of a bipartisan agreement, which would be necessary to have an orderly appropriations process not only this year but next year as well,” the Kentucky Republican told reporters.

The future of the House bill became increasingly unclear Tuesday morning after Democrats debated it in a closed-door meeting.

“With no Republican votes, we can only lose 17 votes on anything,” Yarmuth said Tuesday morning. “So, obviously, any caucus can bring down anything on any bill. We have to figure out if we are going to be able to govern or not. This is our first test of it.”

Yarmuth said that if Democrats can’t agree among themselves, it “minimizes our leverage” in negotiations with the Senate and the White House.

Hoyer rejected the idea later that Democratic infighting on spending gives Republicans more leverage.

“No, I don’t think it gives them any more or less leverage. They have leverage,” he said. “We have to come to an agreement.”

The division over the budget caps among Democrats resembles years’ worth of fights that Republicans had with members of the tea party and the conservative House Freedom Caucus.

Yarmuth joked that “it’s like looking in the mirror.”

Rep. Pramila Jayapal, the other co-chair of the Congressional Progressive Caucus and a leading voice in the fight to increase domestic spending in the caps deal, circulated a letter urging her colleagues to support the progressive effort.

In it, the Washington state Democrat called for support of an amendment to increase non-defense discretionary spending caps by an additional $33 billion for the next fiscal year to “ensure that base levels of defense and non-defense discretionary (NDD) spending are equivalent.”

“Because Congress has not adequately funded NDD priorities, many programs that families rely on are under-resourced,” wrote Jayapal, along with a handful of other progressive members including Pocan and Reps. Ilhan Omar of Minnesota and Adam Smith of Washington state. They added later in the letter, “National security requires critical investments at home too.”

Hoyer stressed to reporters earlier Tuesday that Democratic priorities will be laid out in their appropriations bills this summer.

CNN’s Ted Barrett contributed to this story.