WASHINGTON -- On the brink of power, House Republicans challenged President Barack Obama on Tuesday to join them in a drive to cut federal spending, ban earmarks for favored projects and overhaul the nation's tax code.

At the same time, incoming Majority Leader Eric Cantor, R-Va., conceded that the new GOP majority intends to bypass its own new rules when it votes next week to wipe out the health care legislation approved by Congress last year.

"We just need to repeal it," Cantor said of the effort to fulfill one of the party's main campaign promises from last fall.

Republicans, their ranks expanded by tea-party-backed freshmen, will take control of the House when the 112th Congress convenes at noon today.

One of the first orders of business will be the election of Ohio Republican John Boehner as speaker, replacing California Democrat Nancy Pelosi.

Across the Capitol, Democrats retained their Senate majority in the November elections. But the 60 Senate seats they controlled two years ago, enough to push through much of Obama's agenda, will fall to 53.

That will make it harder to enact legislation Obama still seeks, but it gives them more than enough clout to block passage of bills such as the health care repeal that House Republicans desire.

And it leaves Republicans with leverage to bargain for a reduction in spending on such measures as a $1.4 billion food safety measure Obama was signing during the day.

Obama, speaking with reporters aboard Air Force One as he flew home from a year-end vacation in Hawaii, predicted that Republicans would "play to their (political) base" initially.

He added, "But I'm pretty confident that they're going to recognize that our job is to govern and make sure that we are delivering jobs for the American people."

He said the two sides can build on the lame duck session of Congress in December, when they agreed on a compromise to prevent income taxes from rising, to extend unemployment benefits and to enact a Social Security tax cut that took effect Saturday.

Cantor challenged Obama in a news conference in which he said the GOP envisions a "cut and grow majority" to reduce government spending and regulations and benefit the economy.

The first spending-cut vote is set for Thursday, a 5 percent reduction in the amount ticketed for lawmakers' and committees' offices as well as leadership staff.

Aides estimated the savings at $35 million over the next nine months.

Republicans have pledged to vote at least once a week on bills that cut spending.

Obama is expected to deliver his State of the Union Address before a joint session of Congress on Jan. 25, and Cantor said he was "looking to see some significant spending cuts proposed by the president that we can work on together."

He also said he hopes Obama will prevail on Senate Democrats to ban earmarks, which are funds dedicated to specific pet projects of individual lawmakers.