There are not enough votes in the House to raise the debt ceiling without language attached requiring more spending cuts, Republican leaders said Monday. 

"My members won't vote to increase the debt limit unless we take serious steps in the right direction," Speaker John BoehnerJohn BoehnerBottom Line Trump, GOP fumble chance to govern ObamaCare gets new lease on life MORE (R-Ohio) said during an interview on Fox News. 

BoehnerJohn BoehnerBottom Line Trump, GOP fumble chance to govern ObamaCare gets new lease on life MORE acknowledged that not lifting the debt limit will have "serious consequences for the worldwide economy," but said his conference is not ready to "roll over" on the vote.

Rep. Peter Roskam (Ill.), the House GOP's chief deputy whip, indicated there is a very large bloc of lawmakers opposed to raising the debt ceiling without conditions. He said he could only see it being lifted by a narrow amount without significant restrictions on spending. 

"There are not the votes in the House to raise the debt ceiling," Roskam said on WLS Radio in Chicago. "If the vote were — if the debt ceiling gets raised without any other [conditions on spending attached], there is no way it gets raised by a wide margin." 

Even budget plans released by the GOP would require lawmakers to raise the debt ceiling, making a vote by Congress appear inevitable. House Budget Committee Chairman Paul RyanPaul RyanTrump: Dems ‘will make a deal’ on healthcare Pelosi, more Dems call for Nunes to step aside Nunes will not step down from Russia probe MORE's (R-Wis.) 2012 budget resolution, introduced last week, for example, would not balance the budget until 2040.

Still, the comments by Boehner and Roskam signal Republicans will demand concessions from the administration and Senate Democrats on the debt-ceiling vote, which is expected to be the next big fiscal battle on Capitol Hill. 

The Obama administration has warned that failing to raise the $14.3 trillion debt ceiling by mid-May could have disastrous consequences for the world economy.

In addition, some congressional Democrats are urging leaders to pass a "clean" bill lifting the debt ceiling. 

But Republican leaders have repeatedly demanded that a vote be tied to either a balanced-budget amendment, spending caps or other restrictions on government spending. 

House Majority Leader Eric CantorEric CantorA path forward on infrastructure Democrats step up calls that Russian hack was act of war Paul replaces Cruz as GOP agitator MORE (R-Va.) indicated Sunday that the debt-ceiling vote could be a "leverage" moment for the GOP, similar to the debate over a 2011 budget that resulted in a deal late Friday.

This post was updated at 9:35 a.m.