WASHINGTON — House Republicans on Tuesday staked out what they cast as a middle-ground option in the debate over immigration, pushing an approach that could include legalization but not a path to citizenship, as their Democratic counterparts favor, for the 11 million immigrants in the country illegally.

At a House Judiciary Committee hearing exploring an overhaul of the immigration system, the first of several such hearings expected in the House, Representative Robert W. Goodlatte, Republican of Virginia and chairman of the committee, used much of his time to frame what he called “the question of the day” — “Are there options we should consider between mass deportation and a pathway to citizenship for those not lawfully in the United States?” he asked.

The question was later echoed by Representative Lamar Smith, Republican of Texas and a former chairman of the committee, when he asked Mayor Julián Castro of San Antonio, “Do you see any compromise area between the current status quo and a path to citizenship?”

Mr. Castro, whose twin brother, Representative Joaquín Castro, is a newly elected Democratic member from Texas, replied that he felt that a compromise was for the pathway to citizenship to be “an earned pathway.”

The Republicans also signaled that they were open to the idea of breaking down immigration legislation into several smaller bills, which would allow them to deal with the question of high-skilled workers, as well as a farmworker program, without addressing what Democrats and immigration advocates say is the larger issue: the 11 million people already in the country.

Representative Spencer Bachus, Republican of Alabama, for instance, said he thought the panelists could all agree that “it’s going to be a much easier lift to solve the problem of highly skilled workers.”

“When you take comprehensive, then we’re dealing with certain issues like full citizenship,” he said. “And whatever else we disagree on, I think we would agree on that that’s a more toxic and contentious issue, granting full amnesty.”

Immigration advocates, who had been eagerly awaiting the hearing for a hint of the tone of the debate on immigration as it unfolds in the House, said the use of the word “amnesty” would probably be a bad sign for those in favor of a comprehensive overhaul.