WASHINGTON — President Obama’s aggressive Inaugural Address on Monday presented Congressional Republicans with a stark choice over the next two years: accommodate the president’s agenda on immigration, guns, energy and social programs and hope to take the liberal edge off issues dictated by the White House, or dig in as the last bulwark against a re-elected Democratic president and accept the political risks of that hard-line stance.

As Mr. Obama’s second term begins, Republican leaders appear ready to accede at least in the short term on matters like increasing the debt limit.

Their decision shows that even among some staunch conservatives, Mr. Obama’s inauguration could be ushering in a more pragmatic tone — if not necessarily a shift in beliefs. From the stimulus to the health care law to showdowns over taxes and spending, Republicans have often found that their uncompromising stands simply left them on the sidelines, unable to have an impact on legislation and unable to alter it much once it passed.

Even in the budget impasses that forced spending cuts sought by conservatives, the Republicans’ ultimate goals — changes to entitlement programs and the tax code — have been out of reach.