When pressed by Hoyer on whether the process would be an open one that allows various amendments to be considered, Cantor indicated it would be. "We are hoping that we can have a deliberate debate around the substance and policy of the issues," he said.

The House Appropriations Committee this week released details of the two spending bills, the first of the year. The CJS bill funds the Departments of Commerce, Justice and other agencies, and would provide $51.1 billion in funding, $1.6 billion below the FY 2012 level.

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The Energy & Water bill would spend $32.1 billion, $88 million higher than the last bill, although Republicans point out that if budget rescission from the last bill are ignored, the FY 2013 bill comes in at $623 million less.

Hoyer told Cantor that Democrats remain opposed to the Ryan budget, which is serving as a guide for the appropriations bills that are being developed for 2013.

"We think it's going to be very difficult, frankly, to bring appropriation bills to the floor under the constrains that have been imposed, and we regret … very much that we did not follow the agreement," Hoyer said. Hoyer was referring to the Budget Control Act (BCA), which set spending levels for a decade but which Republicans dipped below in the Ryan budget the House has approved.

Cantor reiterated that Republicans see the BCA numbers as a top line number that cannot be exceeded, but one that can also be shorted if new savings can be found.

"It is our perception that what the deal was in August … was a ceiling, and that we want to try in every way we can to save taxpayer dollars," he said.

During their colloquy, the two leaders also touched on the schedule for next week, which Cantor said will likely include a motion to conference with the Senate on the federal highway bill.

"We have every intention of going forward" with a motion to conference, Cantor said in response to a question from Hoyer. "At this point, I don't know what could come up and preclude us from doing so."

The House on Wednesday approved a short-term highway bill that many Democrats saw as a welcome sign that a conference would happen soon, and House Transportation & Infrastructure Committee Chairman John Mica (R-Fla.) said he would push for a conference soon.

Cantor also said the House will consider cybersecurity legislation, including H.R. 3523, a bill introduced by House Permanent Select Committee on Intelligence Chairman Mike Rogers (R-Mich.).

In light of the Thursday vote in favor of a small business tax cut, Hoyer asked Cantor whether the Ways & Means Committee might soon have a tax bill that reflects the Ryan budget. Cantor answered that "tax reform doesn't come easy," and said it remains to be seen what Ways & Means produces.