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House Speaker John Boehner, on the heels of an election that left the balance of power in Washington unchanged, made the first move in crafting the framework for a deal to potentially avert the so-called "fiscal cliff."

The speaker, on a phone call with Republicans, said he'd like a "bridge" measure to get negotiators past the looming year-end deadline that would, if left un-addressed, trigger automatic spending cuts and tax hikes, people familiar with the call told Fox News.

Separately, Boehner told reporters he wants to then see "major solutions" in 2013 "that begin to solve the problem."

He said Republicans are willing to accept "new revenue," while indicating that doesn't mean higher tax rates. Rather, Boehner said his party is willing to bring in more revenue by closing loopholes and ending certain deductions through comprehensive tax reform -- but only if Democrats are willing to deal, by making serious spending cuts and putting entitlements on the table.

"In order to garner Republican support for new revenues, the president must be willing to reduce spending and shore up the entitlement programs that are the primary drivers of our debt."

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The push to craft a short-term bill, though, could end up creating yet another future deadline that lawmakers wait until the eleventh hour to address. Short-term measures have become a go-to solution for a gridlocked Congress -- with the body repeatedly passing budget bills known as "continuing resolutions" in lieu of a full-scale budget.

The need for renewed fiscal talks grew in urgency after Tuesday's elections did little to change the dynamic in Washington, with Democrats holding on to the White House and Senate and Republicans keeping control of the House. A deal has so far been held up by a central sticking point -- whether to extend all the Bush-era tax rates, or let them lapse for those making $250,000 and up.

Both sides have pledged in the aftermath of the election to work together, but for the past two years bipartisan cooperation has been virtually non-existent.

Boehner, in the Republican House leaders' call with members, expressed concern about getting major legislation passed in a lame-duck session, making a short-term measure more reasonable until the new Congress is sworn in.

However, he also spoke to the Republicans' broader agenda in comments to reporters Wednesday afternoon, saying new revenue is on the table as long as it comes through tax loophole reform, not rate hikes.

House Majority Leader Eric Cantor also spoke out Wednesday on Republicans' goals for the new session, saying in a letter to House Republicans that though the party and the president don't agree on many issues, it was their duty to come together and work for the American people.

"Our task is to legislate based on our principles and forge the compromise that will be necessary to get our nation back on track," the letter said.

However, he also said that the GOP would stick to their principles when dealing with the "fiscal cliff," and would push for a fundamental reform of the tax code rather than increasing taxes.

In the Senate, Majority Leader Harry Reid said Wednesday that "we need to start working together, a lot. Gridlock is not the solution."

Even so, he disputed Boehner's contention that the public doesn't support a tax increase, saying the election was a "mandate ... that the richest of the rich have to help a little bit."

"I'm going to do everything within my power to be as conciliatory as possible. I want to work together, but I want everyone to also understand, you can't push us around," Reid said, adding: "I think we should just roll up our sleeves and get it done."

The Bush-era tax rates are just one of a handful of problems facing President Obama and the lame-duck Congress. Obama and the Democrats want to let the lower rates expire for top income earners, while Republicans want to preserve the existing rates for everyone. If they can't compromise, all tax rates will increase.

Separately, steep automatic cuts to defense and social spending are set to kick in automatically in January, something both sides say they don't want even though they agreed to the cuts in 2011 as an incentive to get negotiators to strike a long-term deficit-reduction deal. That deal never came, leaving the country at risk of federal cuts that some fear could bring the country back into a recession.