House Republicans have introduced a measure to soften the potential damage of those across-the-board spending cuts.

The move would give the Pentagon funding for readiness and ease the pain felt by agencies like the FBI and the U.S. Border Patrol.

The measure would leave keep automatic cuts of 5 percent to domestic agencies and 7.8 percent to the Pentagon, but then award the Department of Defense its detailed 2013 budget.  Other agencies would be frozen in place at 2012 levels.

The GOP funding measure is set to advance through the House on Thursday.

The bill would also head off a potential government shutdown later this month.