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.) acknowledged on Friday afternoon that he is hoping both parties can work together to mitigate the effect of the $1.2 trillion in spending cuts on national defense.

In a colloquy with House Minority Whip Steny Hoyer (D-Md.) on the chamber floor, Cantor stressed that he is not looking to avoid the triggered sequestration cuts, but to reshape them so national defense is not hollowed out, an outcome that Defense Secretary Leon Panetta has warned about.

It is my hope we can act in a bipartisan way to find a way to implement cuts that can replace the across-the-board cuts that will do what I believe is irreparable damage to the Defense Department and our ability to defend this country, Cantor said.

He stressed: Not to avoid the cuts, but to make sure the cuts are there, but not allow them to eviscerate our ability to defend this country.

Cantors proposal could help many Republicans grow more comfortable with the required cuts, as many are now worried about how those cuts would affect Defense spending. Several, particularly some in the Senate, have warned they would fight the required Defense spending cuts.

Hoyer warned Cantor against the idea of dodging the cuts.

If we now walk away from the sequester, as we have walked away from too many agreements in the past … we will again remove the discipline, remove the incentive, remove the imperative … for coming to a bipartisan agreement, Hoyer said.

To that, Cantor stressed again that no one is talking about walking away from fiscal discipline. But he also rejected Hoyers request to consider what the Maryland Democrat called a balanced approach, which Cantor said is Democratic code for raising taxes.

We dont believe that now is the time to raise taxes on small businessmen and women, Cantor said.

He also said that while Republicans and Democrats have a well-known disagreement over whether to raise taxes to reduce the deficit, the parties should focus on areas of agreement. Cantor indicated that this means the GOP prefers to cut what can be cut first, then see what revenues might be needed.

Lets first see if we can fix the problem, Cantor said. Because just paying for things by raising taxes doesnt fix the problem.

But Hoyer countered that the three major bipartisan groups tasked with finding a way forward on deficit reduction have all agreed on the need to increase taxes.