House Republican leaders said Wednesday that the ball was in the Senate's court to avert the fiscal cliff, demanding that the upper chamber take up earlier House-approved bills in a legislative "ping-pong" until the two chambers reach a deal to avert austerity measures set to take effect next week.

In a joint statement, the four leaders said the Senate should at least amend the conservative drafts that the House approved last fall -- one to extend expiring tax cuts for all income levels, the other to shut off automatic spending cuts on national security agencies -- and send them back to the House over the weekend.

With just days left before the Jan. 1 deadline, when the federal government faces a series of tax increases and deep spending cuts, House Speaker John A. Boehner's leadership team has decided that bouncing bills back and forth between the chambers would be the fastest way to reach a compromise.

"They must be amended and returned to the House. Once this has occurred, the House will then consider whether to accept the bills as amended, or to send them back to the Senate with additional amendments. The House will take this action on whatever the Senate can pass, but the Senate first must act," wrote Boehner (R-Ohio), Majority Leader Eric I. Cantor (Va.), Majority Whip Kevin McCarthy (Calif.) and Rep. Cathy McMorris Rodgers (Wash.), chairman of the GOP conference.

The move comes just days after these same GOP leaders failed to secure the Republican votes for Boehner's "Plan B", which would have extended the expiring tax cuts on all income up to $1 million and modified the pending across-the-board cuts to agency budgets by sparing the Pentagon. The statement did not include any guidance as to what measures the House could accept and did not indicate when Boehner would call the House back into session.

Senate Democrats have resisted any attempt to pin the outcome of the budget negotiations entirely on their chamber's next step, suggesting that Boehner has to be a party to some compromise.

“You need a bipartisan agreement here, and the two leading protagonists are the president and Speaker Boehner. If they come to an agreement, it will not be too hard to get the Senate to fall in line," Sen. Charles E. Schumer (D-N.Y.) said as the Capitol shuttered Friday.

Schumer said the “ideal solution” is for a majority from all four party caucuses -- House and Senate Democrats, House and Senate Republicans -- support a final deal. “That’s a middle ground solution that makes the most sense," he said.