Former Vice President Dick Cheney told Republican lawmakers on Tuesday that looming defense cuts could have a serious impact on the U.S. military, even as a new analysis predicted the budget reductions that begin in January could cost 2 million jobs.

Lawmakers on Capitol Hill fretted over how to resolve the issue but remained dug into their longstanding positions. Democrats are calling for increased revenues as well as further budget cuts and Republicans are insisting on spending reductions alone and no new taxes.

Cheney’s visit to the Capitol came as mayors of two major U.S. cities warned that the looming $1.2 trillion federal budget cut is the biggest threat to their local economic recoveries. The 10-year, across-the-board cut is due to go into force on January 2 under a process known as sequestration.

Cheney, who was defense secretary during the first Gulf war and presided over the post-Cold War military drawdown, told Republican lawmakers in a closed-door session the problem should be fixed but made no specific recommendations, said Senator Lindsey Graham.