House Republicans will use the oversight process during the next several months to help identify opportunities to reduce federal spending, Majority Leader Eric Cantor (R-Va.) said Tuesday.

Republicans will outline their plan Wednesday in a set of instructions directing committees to identify ways to reduce the budget to 2008 levels, a key GOP campaign promise from last year. A vote on the instructions to the committees is expected Monday.

While the Appropriations Committee will take the lead on cutting spending levels, the GOP leadership is also asking authorizing committees “to look for spending reductions with the oversight process.”

In his weekly meeting with reporters, Cantor declined to specify which areas the GOP would like to see cut, and no timetable for those reductions has been set. However, Appropriations Chairman Hal Rogers (R-Ky.) will be asked “to recommend how we get [to 2008 spending levels] as quickly as possible,” Cantor said.

Republicans seem to be taking a page out of their Clinton-era playbook, when the GOP used oversight not only as a political bludgeon against the White House but also as a way to constrain regulatory efforts and spending.

Cantor reiterated the warning that Republicans are not inclined to agree to a debt limit increase without substantial cuts to the budget.

He struck a defiant note, warning that if Obama wants the debt limit increase to pass in the House, it will be up to the administration to devise spending cuts to accompany it.

“The president is going to need our votes on that,” he said.