A day after voters endorsed the political status quo in Washington, House and Senate leaders offered conflicting strategies for dealing with the tax and spending issues that have the nation on the brink of a “fiscal cliff.”

While Congressional leaders promised to work with one another to head off tax increases and spending cuts scheduled to begin Jan. 1, prospects for cooperation were dimmed when Speaker John Boehner (R-Ohio) and Senate Majority Leader Harry Reid (D-Nev.) pointed in different directions.

In addition to a fundamental disagreement on taxes, the leaders sent conflicting signals on how much can be accomplished during the post-election session.

Boehner sought to put the ball in President Barack Obama’s court today, offering to accept increased revenue as part of a deficit-reduction deal if the new money does not  come from increased tax rates and if the growth in the cost of entitlement programs is addressed.

Republicans have said additional revenue can be obtained through an overhaul of the tax code and can come from wealthier taxpayers without raising tax rates, perhaps by limiting the use of some tax credits and deductions.

Boehner rejected any notion that the newly re-elected president and Reid — whose party increased its advantage in the Senate on Tuesday — can claim a mandate from voters to allow expiration of the 2001 and 2003 tax rates for those earning more than $250,000.

“The president has called for a balanced approach to the deficit — a combination of spending cuts and increased revenues,” Boehner told reporters. “But a balanced approach isn’t balanced if it means higher tax rates on the small businesses that are key to getting our economy moving again and keeping it moving.”

Boehner said the same thing in a conference call with Republican lawmakers this afternoon, according to two sources with knowledge of the discussion, and said he will be conducting interviews during the next few weeks to drive home his position.

Boehner appealed to House Republicans for unity. The Speaker’s negotiating position was undercut during the past two years when he could not muster the support of a majority of his Conference for bipartisan deals, particularly those dealing with fiscal issues. If he cannot deliver 218 votes, he told members of his Conference, Democrats will run the show in negotiations.

Reid, who spoke with Boehner this morning, said neither leader should draw lines in the sand and signaled he thinks Democrats do indeed have a mandate from Tuesday’s election to raise taxes for those with very large incomes.

 “Look at all the exit polls, look at all the polling, the vast majority of the American people — rich, poor, everybody — agrees that the rich — richest of the rich — have to help a little bit,” Reid said. “People who are making more than a million dollars a year, the vast, vast majority of them are happy to pay that. The only place that people disagree are Republicans in Congress.”

Obama phoned Boehner and Reid  to discuss the fiscal cliff situation. He also placed calls to House Minority Leader Nancy Pelosi (D-Calif.) and Senate Minority Leader Mitch McConnell (R-Ky.), according to the White House.

Reid and Boehner were also on different pages today regarding the timing of a possible fiscal deal. While Reid said enough work has been done to allow action during the post-election session that begins next week, Boehner and other Republicans favor a short-term deal laying the groundwork for a broader solution  next year.

“We won’t solve the problem of our fiscal imbalance overnight in the midst of a lame-duck session of Congress,” Boehner said today. “And we certainly won’t solve it by simply raising tax rates or taking a plunge off the fiscal cliff.”

While a major tax overhaul would likely be beyond the scope of a lame-duck session, the chairmen of the Congressional tax-writing committees said today they are ready to work on such a project.

“We need to put progress ahead of politics and work towards a compromise that provides some certainty to American families and businesses,” said a statement from Senate Finance Chairman Max Baucus (D-Mont.), who would be Reid’s point man on any rewrite of the tax code. “We need to craft a proposal that supports jobs, expands opportunity and puts America’s economy back on track.”

Similarly, House Ways and Means Chairman Dave Camp (R-Mich.) said in a statement that a tax overhaul that avoids raising rates could be a victory for both parties.

“There is bipartisan support for tax reform that closes loopholes and lowers rates,” he said. “I believe the House and Senate are prepared to act next year on reform, and that not only means a fairer tax code and more jobs, but also more revenue to help solve our nation’s debt and deficit problems.”

A tax overhaul modeled on the 1986 law would run into resistance from some Democrats unless it raised revenue needed to head off cuts in federal programs.

“We must reduce the deficit, which is strangling our economic growth,” Senate Democratic Conference Vice Chairman Charles Schumer (N.Y.) said before the elections. “And we must seek to control the rise in income inequality, which is hollowing out the middle class.”

 Schumer argued in an Oct. 9 speech that a tax overhaul without effective increases in taxes paid by upper-income taxpayers would not help solve those problems.