WASHINGTON (Reuters) - A top Republican refused on Sunday to rule out the possibility of a government shutdown next year over growing federal deficits but said if there were one, President Barack Obama would bear responsibility.

House Minority Whip Rep. Eric Cantor (R-VA) presents U.S. Senate candidate Marco Rubio (R-FL) during Rubio's campaign event in Fort Lauderdale, Florida July 31, 2010. REUTERS/Carlos Barria

House of Representatives Republican Whip Eric Cantor said it’s up to Obama to work with Republicans since they won the House from Obama’s Democrats in last week’s election, vowing to slash spending and shrink government.

Appearing on “Fox News Sunday,” Cantor focused on Obama when asked if Republicans could provide assurances that they wouldn’t let the government shut down in any confrontation with the White House, disrupting all but the most essential services to millions of Americans.

“The president’s got a responsibility as much or more so than Congress to make sure that we are continuing to function in a way that the people want,” Cantor said.

“This president certainly, as in his own words, took a shellacking by the voters” in Tuesday’s election that saw Republicans take the House and cut the Democratic majority in the Senate, Cantor said.

“It is time for him to try and come meet us and say, ‘Fine, let’s get back to the kind of things that Americans are about. It is living within our means,’” said Cantor, in line to become majority leader when the new Republican House convenes in January.

As majority leader, Cantor would be the Republican’s No. 2, behind only John Boehner, expected to become the chamber’s new speaker, replacing Democrat Nancy Pelosi.

The U.S. budget deficit for the fiscal year that ended September 30 was about $1.3 trillion, with the U.S. debt topping $13 trillion. Congress must decide next year whether to raise the $14.3 trillion debt ceiling to avoid a U.S. default.

At the same time, if the White House and Congress can’t agree on new spending plans, there could be a government shutdown.

Obama inherited a deep recession when he took office in January 2009 and within months got fellow Democrats in Congress, over a wall of Republican opposition, to pass an unprecedented $814 billion economic stimulus package.

The economy is growing again, but unemployment has risen, reaching a stubbornly high 9.6 percent.

House Republicans aim to slash spending by $100 billion next year, pushing it back to 2008 levels, with exceptions for programs for the elderly, the military and veterans.

They are being pressured to cut costs by the anti-establishment Tea Party movement that helped them make big gains on Election Day.

Republicans also vow to begin to “repeal and replace” Obama’s healthcare overhaul by denying funding to fully implement it.

EARLIER SHUTDOWN BACKFIRED

These plans have brought back visions of spending battles that led to a government shutdown in 1995 after Republicans won the House from President Bill Clinton’s Democrats. That shutdown backfired politically on the Republicans, helping position Clinton win re-election the following a year.

House Republicans are determined not to make political missteps that give Democrats a boost in 2012.

Republican Senator-elect Rand Paul, a Tea Party favorite, told ABC’s “This Week,” that his top aim is to trim the federal debt,

“We have to do something about the debt. I think we’ve been fiscally irresponsible for a generation or more here,” he said.

Senate Republican Leader Mitch McConnell, who has said his leading goal is to deny Obama re-election in 2012, said, “We hope to do business with the president on a number of things.”

One area is whether to increase all or some of Bush-era tax cuts -- for the middle-class as well as wealthier Americans, including many small business owners -- set to expire at the end of this year.

Obama called a Republican proposal to extend tax cuts to wealthier Americans for two years a “basis for conversation” and said he sees a potential for compromise.

In an interview on the CBS show “60 Minutes” to air on Sunday night, he said his top priority was making sure taxes did not rise on Americans making less than $250,000 a year.

Extending tax cuts could swell the federal debt. But Republicans argue that allowing the tax cuts to expire would hurt economic growth.

“The issue here is whether you want to raise taxes on small businesses in the middle of what most Americans think is a recession,” McConnell told CBS’s “Face the Nation.”

“I and all of my members think it’s a bad idea to do that. I do sense some flexibility on the president’s part and we’re happy to talk to him about it,” McConnell said.