House Majority Leader Eric CantorEric Ivan CantorThe Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Race for Republican Speaker rare chance to unify party for election Scalise allies upset over Ryan blindside on McCarthy endorsement MORE (R-Va.) said Wednesday that House Republicans will not consider a fiscal deal with Democrats that eliminates some of the sequester cuts by raising taxes.

The sequester cuts that applied to discretionary spending caused problems for Republicans this year, and forced GOP leaders to pull one of their 2014 spending bills from the House floor when too many Republicans opposed the cuts.

But in a colloquy with Minority Whip Steny Hoyer (D-Md.), Cantor said that did not mean Republicans would be looking to raise taxes when the House and Senate meet to hash out differences on 2014 spending levels. Instead, he repeated that the GOP will try to win cuts to mandatory programs.

"The Republicans in the majority in the House do not believe we ought to raise taxes, and we will not go about raising taxes in exchange for sequester relief," he said. "What we want to do instead is to allow for sequester relief and put into law mandatory savings that in the long run will exceed the kind of spending reductions that are in the sequester."

That position puts the two parties back in the same boat they've been in since Republicans took over the House in 2010 — the GOP has insisted on spending cuts, while Democrats have looked to trim the budget deficit with tax increases. Hoyer indicated that this disagreement would come up again, by noting that the House-Senate conference will have to somehow find a way to compromise on the two bills.

Cantor said he's hopeful that some deal is possible, and said the chances go up if the two parties find a way to focus on areas where they agree. "If that spirit of negotiations is adopted by both sides, I believe there could be progress on the farm bill as well as other issues," he said.

Hoyer pressed Cantor to commit to reaching a 2014 spending deal before Thanksgiving, which he said would help Congress avoid another threat of a shutdown in early January, when temporary funding runs out. But Cantor was noncommittal.

"I agree … that it is desirable, and I look at it as a priority that we allow for the … appropriations process to begin again," he said. "But that will require us to arrive at an agreement on what that top-line number is."

Cantor said he expects the House to consider a conference report on the farm bill before the end of the year, as well as some legislation on immigration. But he again said the House would not take up the Senate's immigration bill, a sign the House bill or bills will focus primarily on border enforcement, not the creation of a pathway toward citizenship for illegal immigrants.

"We are not going to consider the Senate bill because we object to the Senate bill, although we do want to make some progress on reforming the broken system," he said.

Cantor added the House will likely consider bills aimed at increasing the domestic energy supply, a National Defense Authorization Act, and provisions that will expire before the end of the year. He added that the GOP would continue to focus on ObamaCare implementation, but did not say the House would take up legislation in this area.