WASHINGTON — With Congress unlikely to stop deep automatic spending cuts that will strike hard at the military, the fiscal stalemate is highlighting a significant shift in the Republican Party: lawmakers most keenly dedicated to shrinking the size of government are now more dominant than the bloc committed foremost to a robust national defense, particularly in the House.

That reality also underscores what Republicans, and some Democrats, say was a major miscalculation on the part of President Obama. He agreed to set up the automatic cuts 18 months ago because he believed the threat of sharp reductions in military spending would be enough to force Republicans to agree to a deficit reduction plan that included the tax increases he favored.

“Fiscal questions trump defense in a way they never would have after 9/11,” said Representative Tom Cole, Republican of Oklahoma. “But the war in Iraq is over. Troops are coming home from Afghanistan, and we want to secure the cuts.”

Representative Howard P. McKeon of California, the chairman of the Armed Services Committee and one of the lawmakers Democrats had hoped would never accept the military cuts, went almost as far. “Republicans aren’t cookie cutter,” he said, “but we do agree on the basic premise of where we’re trying to go. And if we don’t get our fiscal house in order, it’s very hard to provide for the defense of the nation.”