The Boston City Council deadlocked on a call to reject Mayor Michelle Wu’s proposed $4.9 billion budget, killing a bid from some councilors to put pressure on Wu to increase spending in a way that would prevent painful cuts.

Councilor Brian Worrell, the Ways and Means chair last term, called for the Council to reject the mayor’s budget on Wednesday — going against the recommendation of Councilor Ben Weber, the Ways and Means chair this term, who sought to keep the budget in committee for further discussion.

“For me, this is about whether the Council will use all the tools that we have before us to fight for what we’ve heard over the course of a month and a half,” Worrell said. “Residents have been clear they do not want fewer youth jobs, less housing support, or cuts to food justice, arts and culture, veteran services, age strong or the complete defunding of human rights.

“While services are being cut, homeowners are still facing double-digit property tax increases. People are being asked to pay more and get less, and that is a hard message to defend,” Worrell added. “The public came here asking us to use our power today. Using our power means sending this budget back and asking for a stronger one.”

Worrell’s call came after Mayor Wu issued a rebuke to councilors considering voting down her budget last Thursday, saying she would not increase spending and that requests for her to do so were “fiscally irresponsible.”

Weber, an ally of the mayor, cited the mayor’s comments when speaking against the effort to reject the budget, saying that the Council risks having Wu come back with a reduced spending plan due to lower state aid projections than initially anticipated, and losing its ability to amend the mayor’s budget.

The Council has the authority to amend, but not increase the overall budget, by moving money around between or within departments. Weber said the Council should stick to the amendment process, rather than look to “artificially inflate” revenue or spend from the city’s $1.7 billion reserve fund.

“The mayor’s made it clear that she will just resubmit the budget or a smaller one because state aid is less than expected,” Weber said. “Unlike under Menino or Flynn or White, the mayor doesn’t need our support. It is our job, if we have a problem with the budget, to amend it and override her vetoes if we have nine votes.

“So, a rejection now would be a gesture, just one with potentially serious consequences, and the hard work will still remain for us to do one week from now,” Weber said. “I deeply respect the advocates who have helped come up with these ideas, and I share the same goal — restore as much of the grant funding as possible — but I don’t want that to come at the expense of our financial future.”

Worrell argued that rejecting the budget early on would still allow the Council to go through the amendment process, given that the body has until June 10 to submit its amendment package to the mayor for consideration.

“We don’t lose anything by rejecting this budget,” Worrell said. “I don’t know what the mayor will do, but there’s an opportunity for all of us working together to make this budget better, and the only way that the mayor can help out in that process is if we send it back.”

Ultimately, Worrell’s call for a vote to reject the budget failed, as he needed a two-thirds majority, or nine votes, to allow the matter to be taken up.

The Council deadlocked, 6-6, to allow Worrell’s motion to reject the budget to come to a vote, in a split that’s become common this term, between Wu’s council allies and others who are either critics of the mayor or aren’t necessarily Wu allies.

Lining up behind Worrell were Councilors Miniard Culpepper, John FitzGerald, Ed Flynn, Julia Mejia, and Erin Murphy. Backing Weber were Council President Liz Breadon and Councilors Sharon Durkan, Ruthzee Louijeune, Enrique Pepén, and Henry Santana. Gabriela Coletta Zapata was absent.

The vote to block the matter from official consideration came after more than an hour of debate.

All councilors, depending on where they stood on the vote, expressed concern about the cuts that have been proposed in the mayor’s budget, which Worrell cited when urging his colleagues to vote it down.

“No one has got up and said this is a good budget, but we can’t get to nine to reject what everyone has said,” Worrell said.

Durkan said her vote was about “fiscal responsibility.”

“I can see places for cuts, and I can see places for restoration,” Durkan said.

FitzGerald, on the other hand, said his vote was about looking out for the financial future of the city.

“The City of Boston is on shaky financial ground, and the projections that we see … show even less and less growth and even less and less revenue,” FitzGerald said. “It is our duty to apply pressure to the administration when we see that the City of Boston is trending in the wrong direction.