WASHINGTON — Congressional Republicans are preparing to counter increasingly dire warnings from President Obama about the impact of automatic budget cuts with a plan to give the administration more flexibility in instituting $85 billion in cuts, a proposal they say could protect the most vital programs while shifting more of the political fallout to the White House.

The plan is vigorously opposed by the administration, which said Monday that it would do little to soften the blow to military and domestic programs. But it is also dividing Democrats, with lawmakers from the states facing the deepest cuts signaling that they may be prepared to go along with Republicans if it means avoiding indiscriminate cuts to military programs and social services.

With just three days left until the across-the-board cuts called sequestration are scheduled to begin, administration officials continued to describe the consequences in alarming terms, even as there was little evidence of serious negotiations with lawmakers to reach a deal to avoid them.

Still, Senator Lindsey Graham, a South Carolina Republican and a leading defense hawk, appeared to advance the debate on Monday. “This is the chance to do the big deal,” he said on CNN. “I’m willing to raise revenue. I’m willing to raise $600 billion in new revenue if my Democratic friends would be willing to reform entitlements, and we can fix sequestration together.”