WASHINGTON — As the House and Senate return in full from a recess on Tuesday, Republican lawmakers may try to run — and some will — but they cannot hide from the question that is likely to dog them until Election Day: How do they solve a problem like Donald J. Trump?

Republican members of Congress, guided by a complicated soup of regional interests, constituent pressure and inner moral voices, will be hard pressed to avoid taking a position on Mr. Trump now that he is their presumptive presidential nominee.

While lawmakers were on recess last week, Mr. Trump seized control of the Republican Party after winning the Indiana primary and pushing his last rivals out of the race. But the House speaker, Paul D. Ryan, Republican of Wisconsin, has said he was “not ready” to endorse him, expressing concerns about his tone and values.