Hoyer pressed Cantor several times to commit to a clean debt ceiling increase, something that will have to happen by mid-May to avoid exceeding that ceiling. "I'd hope we can get to a place where we say the debt limit is not going to be subject to political maneuvering," Hoyer said.

Cantor offered few specifics, but Republican leaders have said they would again seek more spending cuts in the context of an increase in the debt ceiling. Cantor stressed that Congress needs to start enacting policy choices that result in reduced deficits and a smaller national debt.

"I do think that we should be mindful of how we're going to tell the public we're going to go into the future and pay off these debts," Cantor said.

The government has the potential to bump up against the ceiling in May. Earlier this year, Congress passed the No Budget, No Pay Act, which suspended the debt ceiling limit through May 18.

On May 19, the debt ceiling will be equal to the level of debt accumulated by that date, which means Congress will be under pressure to act before then to increase the ceiling again.

Earlier this month, Cantor told Republicans that the House would pass a bill soon that ensures federal payments on interest on the national debt would be prioritized in the event that the debt ceiling is hit.

But Hoyer warned Cantor of press reports that say attempts to prioritize spending in this way would lead to another downgrade in the U.S. credit rating.

On other issues, Hoyer asked Cantor if the House would push for a conference with the Senate to agree on a unified budget plan. But Cantor was non-committal on a conference, and said some talks are already underway on how to combine the vastly different proposals.

"I know that [House Budget Committee] Chairman Ryan and [Senate Budget Committee] Chairman Murray are already in discussions about a path forward, and I look forward to the result of those discussions," he said.

While the Cantor-Hoyer weekly colloquy often consists of a partisan back-and-forth, the two leaders today agreed to sit down and discuss possible ways to explore job-related legislation.

Hoyer noted that he has proposed a "Make it in America" agenda that includes a national manufacturing strategy, boosting exports, encouraging companies to create jobs in the United States, and expanding the U.S. energy supply.

"I say all that … to suggest that I would like to sit down with you so that we can talk together about how we mutually can move forward on what … we call a Make it in America agenda, but a jobs agenda," he said.

Cantor agreed, and said he was hopeful the talks could yield some agreement on these issues. He said Republicans have already sought to advance ideas like boosting worker skills and encouraging medical innovation.

"These are the kinds of things I look forward to working on with the gentleman as well, and I accept his invitation and look forward to being able to sit down," Cantor said.