"It is not the intention of this majority leader to bring forward to the floor that bill for several reasons," Cantor said. "First of all ... the notion of increasing tax rates in an economy that's still struggling, where we have entirely too many Americans out of work, is something anathema to a job-creating future.

"Secondly ... raising tax rates, asking Americans, small businesses, to pay more of their money into Washington, when Washington cannot seem to get a handle on its spending problem, will just make matters worse. We've got to stop the spending madness."

Hoyer pushed back and stressed repeatedly that the Senate bill would not raise taxes on anyone, and noted that President Obama has said he would veto legislation keeping in place lower rates for high income.

"The president of the United States has made it very clear — he will not sign a bill that reduces the tax obligations of those over $250,000 in the coming year. He's not going to sign that bill," Hoyer said.

Cantor replied by saying that the tax rates are long-standing disagreement between Republicans and Democrats, and said Republicans are pushing Obama to be more specific about how he proposes to get around the pending tax hike and spending cuts that are known together as the "fiscal cliff."

"We continue to ask this president in these negotiations to be specific with us," Cantor said. "We want to address the problem. We realize that we are digging the hole deeper every day, and that taxpayers are on the run."

The discussion between Cantor and Hoyer is the latest evidence that the two parties remain far apart on how to resolve the fiscal cliff. House Republican leaders this week rejected a proposal from the Obama administration that called for $1.6 trillion in new taxes, with the promise of an undefined $400 billion cut to spending.

Obama also proposed a new $50 billion stimulus plan, and authority to increase the debt ceiling whenever he wants — two other elements that Republicans rejected out of hand.

Cantor announced that as negotiations continue, the House would have a shorter work week next week. Instead of working a full week, the House will be in session from Monday to Wednesday, but he vowed that the House would not adjourn for the year until the fiscal cliff fight is resolved.

In response to another question from Hoyer, Cantor reiterated that Republicans support attempts to approve the Violence Against Women Act reauthorization bill. But he indicated there is still little progress being made in negotiations with the Senate, which has a different version of the bill.

Hoyer also asked whether the House might pass a separate bill funding recovery efforts in the Northeast in the wake of Superstorm Sandy. To that, Cantor replied only that last year's Budget Control Act set up a formula for determining money available for disaster relief, and that the Federal Emergency Management Agency (FEMA) should make its recovery cost estimates before Congress takes any further action.

Cantor also said he would look at a resolution expressing condolences for those affected by Sandy, which was introduced by Rep. Jerrold Nadler (D-N.Y.).