WASHINGTON (AP) — As Congress wrestles with immigration legislation, a central question is whether the 11 million immigrants already in the United States illegally should get a path to citizenship.

The answer from a small but growing number of House Republicans is “yes,” just as long as it’s not the “special” path advocated by Democrats and passed by the Senate.

“There should be a pathway to citizenship — not a special pathway and not no pathway,” Rep. Jason Chaffetz, R-Utah, told ABC 4 Utah after speaking at a recent town hall meeting in his district. “But there has to be a legal, lawful way to go through this process that works, and right now it doesn’t.”

Many House Republicans say people who illegally crossed the border or overstayed their visas should not be rewarded with a special, tailor-made solution that awards them a prize of American citizenship, especially when millions are waiting in line to attempt the process through current legal channels.

It’s far from clear, however, what a path to citizenship that’s not a special path to citizenship might look like, or how many people it might help.

The phrase means different things to different people, and a large number of House Republicans oppose any approach that results in citizenship for people now are in the country illegally. Some lawmakers say such immigrants should be permitted to attain legal worker status, but stop there and never progress to citizenship. That’s a solution Democrats reject.

Nonetheless, advocates searching for a way ahead on one of President Barack Obama‘s second-term priorities see in the “no special path to citizenship” formulation the potential for compromise.

“I think there’s a lot of space there,” said Clarissa Martinez, director of civic engagement and immigration at the National Council of La Raza. “And that’s why I’m optimistic that once they start grappling more with details, that’s when things start getting more real.”

Once Congress returns from its summer break the week of Sept. 9, the focus will be on the GOP-led House. The Democratic-controlled Senate in June passed a far-reaching bill that includes a big, new investment in border security and remakes the system for legal immigration system, in addition to creating a 13-year path to citizenship for those already here illegally.

House Republicans have rejected the Senate approach, promising to proceed instead with narrowly focused bills, starting with border security. No action is expected on the House floor until late fall, at earliest, because of pressing fiscal deadlines that must be dealt with first.

The timing crunch, along with the significant policy and process disagreements, has left some supporters pessimistic about the future of immigration legislation. They find hope, however, in some recent comments from House Republicans around the country suggesting they could support a solution that ends in citizenship at least for some who now lack legal status.

Democrats, some Republicans and most outside immigration advocates are pushing for a relatively straightforward path to citizenship like the one in the Senate.

It imposes certain restrictions, seeks payment of fees, fines and taxes, and requires that prospective immigrants attempting the process legally are dealt with first. Once those criteria are met, most people here illegally could get permanent resident green cards in 10 years, and citizenship in three more. Agriculture workers and immigrants brought to this country as children would have a quicker path.

That approach is rejected by most House Republicans as a “special” path to citizenship.

“It’s not a bill I can support,” House Judiciary Committee Chairman Bob Goodlatte, R-Va., said at a Verona, Va., town hall meeting recently. “We think a legal status in the United States, but not a special pathway to citizenship, might be appropriate.”

Goodlatte has said that after attaining legal status, immigrants could potentially use the existing avenues toward naturalization, such as family or employment ties.

He and others also argue that many immigrants would be satisfied with legalization alone, without getting citizenship. That’s something many advocates dispute, though studies show that a significant number of immigrants who are eligible for citizenship haven’t taken that step — about 40 percent in a Pew Hispanic Center study in February.

Goodlatte has not provided much detail on how he foresees immigrants moving through existing channels from legalization to citizenship. Depending on its design, such an approach could touch anywhere from hundreds of thousands to many millions of the 11 million people here illegally. So if House Republicans end up taking that approach, how they craft it would help determine whether Democrats and the advocacy groups could go along.

For now, advocates say that making immigrants here illegally go through the existing system would help relatively few of them.

Current law says that if you’ve been in the country illegally for more than a year, you have to return to your home country for 10 years before you can re-enter legally, which would likely dissuade many people.

Moreover, existing family sponsorship channels are badly backlogged, and many are capped. People applying for citizenship through their siblings face waits of more than 20 years in some cases, for example. On the employment side, existing visa programs are difficult to use and inadequate to meet demand, and also face long backlogs.

Waiving the requirement for people to exit the country and adding visas to reduce backlogs could take in a substantial number of the 11 million here illegally, arguably without being a “special” pathway, advocates say.

It’s a long shot, but the result could be an immigration deal between the House and the Senate, and a bill for Obama to sign.

“If the House wants to dis the Senate bill and come up with their own approach to the 11 million that has no special pathway to citizenship, we would be happy to work with them on a way that would meet with our bottom line, which is an inclusive, immediate path to legal status for the 11 million, and an achievable and clear path to eventual citizenship,” said Frank Sharry, executive director of America’s Voice, a pro-immigrant group. “They can preserve the sound bite and we can have the policies that we want.”