House Republican leaders are discussing whether to pursue an omnibus appropriations bill or tackle the issue in three or four separate bills, even as the Senate readies its own set of combined appropriations measures that could see floor action as soon as Thursday.

A House Appropriations Committee aide said the Senate legislation, which will combine the Transportation and Housing and Urban Development; Agriculture, rural development and Food and Drug Administration; and Commerce, Justice and science appropriations bills, is not related to ongoing negotiations between the two chambers.

But the Senate bill mimics an approach still on the table in the House — to pass three or four bills that combine several appropriations bills each.

This “minibus” tack would avoid the political bruises likely to ensue from passing an omnibus bill after Republicans harshly criticized one-size-fits-all spending bills in the last Congress and vowed in their “Pledge to America” to “advance major legislation one issue at a time.”

Rep. Jeff Flake (R-Ariz.), for instance, is preparing a letter urging Speaker John Boehner (R-Ohio) not to pursue an omnibus and to bring any appropriations bill to the floor with an open rule.

“An open House has been his hallmark, and it’s a good one,” Flake, a member of the Appropriations Committee, said of Boehner in an interview late Tuesday.

Flake has attracted significant support — around 50 votes — to parallel pushes on prior spending battles.

But the clock is ticking, and the differences between the two chambers are prompting House sources to speculate about a long-term continuing resolution to fill the void.

“The House Appropriations Committee does not support a long-term CR at this time,” a House Appropriations Committee aide said.

Appropriations Committee member Jo Ann Emerson (R-Mo.) noted that the House’s and Senate’s divergent calendars could make it even more difficult for the two chambers to reconcile their appropriations bills.

The House and Senate are scheduled to be in session together for five legislative weeks before the end of 2011.

Further complicating the matter, some in GOP leadership are arguing that a single omnibus bill will give Republicans more leverage in negotiations with Democrats.