WASHINGTON — In the first test of Washington’s new political alignment, President Barack Obama will meet with Republican leaders Tuesday with the nation’s tax rates and a nuclear arms treaty in doubt.

Neither side expects final deals from an hour-long encounter, but the sparring could have major consequences, both short- and long-term.

The expiring Bush-era tax cuts are the most pressing matter. Without quick action, taxpayers face sharp increases next year as the rates return to levels set during the Clinton administration. Discussions are expected to center on a temporary extension that would put off the partisan clash over the biggest disagreement – whether to permanently extend current rates to all or to raise them for higher-income taxpayers.

The private, late-morning White House meeting with top lawmakers from both parties is fraught with potential and hazards, both for the immediate work left before Congress adjourns this year and for the relationship between Obama and congressional Republicans over the next two years.

Republicans caught a wave of voter disenchantment with the economy on Nov. 2 and wrested control of the House from the Democrats. They also expanded their minority in the Senate.

The new lineup presents a dramatically different dynamic for Obama. Though he pledged to bridge partisan divides during his presidential campaign, he ended up passing the big initiatives of his first two years with virtually no Republican support.

“My hope is that tomorrow’s meeting will mark a first step toward a new and productive working relationship,” Obama said today, “because we now have a shared responsibility to deliver for the American people on the issues that define not only these times but our future.”

That comment came as he announced a two-year pay freeze for civilian government workers, a step hailed by Republicans and sharply criticized by Democratic allies such as the AFL-CIO.

The most immediate challenges for Congress’ postelection lame duck session are considering whether Congress will extend the tax rates and the Senate will ratify a new treaty to reduce nuclear weapons arsenals in the U.S. and Russia represent the most immediate challenges.

Republicans want all the 2001 and 2003 tax cuts to be extended permanently. Obama and Democratic leaders in Congress want to extend them only for individual taxpayers making less than $200,000 and couples making less than $250,000

Rep. Eric Cantor of Virginia, who will become the House majority leader in January, accused the president of engaging in “class warfare.” ”This country is about making sure everyone has a fair shot,” he said in an interview.

Obama and his top aides have insisted that he won’t approve an extension of upper income rates that is permanent, a potential opening for a short-term extension.

Democrats are themselves divided on the tax rate question, with some arguing no taxes should be allowed to increase during a weak economic recovery. At the same time, a number of liberal millionaires have weighed into the debate, arguing they shouldn’t benefit from a continuation of their current rates.

Sen. Ben Nelson of Nebraska, a conservative Democrat who is often in the middle of Senate legislative bargains, said all tax cuts should be extended for at least two years but that making them permanent would put too great a strain on the federal deficit. Republican senators including South Carolina’s Lindsey Graham and Jim DeMint, the latter a hero of the tea party movement, say a temporary extension of the tax rates might be the best they can get.

Despite their political gains, Republicans are approaching Tuesday’s session with some apprehension. Presidents typically gain a public relations advantage by inviting leaders of the opposition party to the White House.

Many Republicans still bristle at last February’s health care summit that Obama called. Democrats got more time to make their case than Republicans, and the session yielded no Democratic compromises.

“In the past, when we have private meeting with the president, he has rarely missed the opportunity to lecture us for our political or ideological beliefs,” Cantor said. “I’m hopeful that those days area gone.”

Obama’s ability to reach compromises is further complicated by the internal politics within each of the parties. The House lost many of its moderates in this month’s elections, leaving behind a more liberal caucus. Republicans, are keenly aware of a tea party movement that punished GOP lawmakers seen as too willing to cross party lines.

Patrick Griffin, who served in the Clinton White House as assistant to the president for legislative affairs, said cooperation will emerge only if the bipartisan White House meetings continue. But he said the tenor set by this meeting will demonstrate whether the two sides can work together.

“The more inflammatory they are, it suggests that we’re in a minimalist strategy for the lame duck and it doesn’t bode well for the opening salvos of the next Congress,” he said.

The White House has repeatedly pointed to remarks by Senate Minority Leader Mitch McConnell, R-Ky., that the main goal of Republicans over the next two years is to assure Obama’s re-election defeat.

“I was dismayed when I saw Sen. McConnell’s comments,” chief White House political adviser David Axelrod said. “There will be plenty of time for elections.”

Axelrod said the message of the election was that the public wants more cooperation. “Those who are perceived as thwarting that will pay a price for it,” he said.

White House officials see incoming Republican Speaker John Boehner as a possible partner. They cite him as a potential broker with other Republicans on legislation that reauthorizes the No Child Left Behind education law. They also say they were encouraged by Boehner’s acknowledgment that Congress will have to confront the question of raising the national debt limit “as adults,” despite opposition from some newly elected Republicans.

“No doubt there are interesting dynamics,” Axelrod said. “There are people who say they want to take steps to deal with our long-term debt issues – we’ll work with anyone who wants to work with us on that in a productive way.”