On the eve of their return to 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 House Majority Leader Eric Cantor, R-Va., conceded the new GOP majority intends to bypass its own new rules when it votes next week to wipe out the health care law approved by Congress last year, according to AP.

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

The AP notes that Republicans, their ranks expanded by Tea Party-backed freshmen, take control of the House when the 112th Congress convenes at noon on Wednesday. One of the first orders of business will be the election of Ohio Republican John Boehner as speaker, replacing Democrat Nancy Pelosi of California.

Earlier in the day, Cantor released a statement detailing a self-imposed operating budget cut for the new Congress.

“Federal spending is out of control, and that’s why we will begin the new Republican Majority by cutting our own Congressional operating budgets,” the statement read. “For too long, families and small businesses across America tightened their belts while the federal government continued its spending spree. That federal spending spree will stop with the new Republican Majority. This self-imposed cut to our own operating budgets in the House will save American taxpayers more than $35 million right away and I hope that federal agencies across the spectrum will follow suit and find ways to cut their own budgets. If not, we’re happy to do it for them.”

Cantor challenged and chided Obama by turn 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.

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

Obama is expected to deliver his State of the Union Address 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."