House Majority Leader Eric CantorEric CantorIf we want to make immigration great again, let's make it bipartisan Top Lobbyists 2017: Hired Guns GOP Rep. Jeb Hensarling to retire after end of current term MORE (R-Va.) on Thursday hinted that the House could take up a bill to defund U.S. military intervention in Libya as early as next week.

Speaking on the House floor, Cantor outlined next week's House schedule, which he said could include "potential legislation related to the ongoing military conflict in Libya." 

Speaker John BoehnerJohn Andrew BoehnerTrump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery One year later, neither party can get past last year's election MORE (R-Ohio) said earlier in the day that the House could move to cut off funding for Libya based on inadequate answers from the Obama administration about the U.S. intervention.

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Neither Cantor's nor John BoehnerJohn Andrew BoehnerTrump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery One year later, neither party can get past last year's election MORE's office had any further comment on the majority leader's remarks.

Cantor also addressed the ongoing debt ceiling talks led by Vice President Biden. He said that while he is "cautiously optimistic" about the progress being made, he also stressed repeatedly that spending cuts must be part of any deal.

"I am hopeful that we can meet or exceed the expectations right now, which is to say we are aiming to reduce spending by the trillions in order for us to engage in the kind of vote-taking that needs to take place to stave off a default," Cantor said. "But I say to the gentleman first and foremost, our side will not support any attempt to raise the debt ceiling that is not accompanied by the kind of cuts necessary and reforms necessary, nor will we support an attempt to raise the debt limit that raises people's taxes."

Cantor made these remarks in a discussion on the floor with House Minority Whip Steny Hoyer (D-Md.), who asked his opinion on the debt-ceiling talks. "We are very hopeful that these talks will prove fruitful and that we can move ahead," Hoyer said.

Hoyer also tried to coax Cantor into agreeing that the debt ceiling must be lifted by early August even if there is no broader deal. "Surely, I would hope the gentleman would agree that allowing America to default on its bills is not an acceptable alternative even if we can't get to agreement," Hoyer said.

Cantor seemed to say in response that both parties need to make sure they are not in a position to be without a spending cut agreement by then.

"By just acting to increase the credit limit of this county without following through on our commitment for spending cuts and reform is just checking the box and is reckless," Cantor said. "That's why I say to the gentleman, it is important for us to come together, to walk together, to make sure that we are able to execute on a plan to reduce spending once and for all and to reform the system here in Washington so that the markets understand we mean what we say."