SACRAMENTO, Calif. -- Backers of a measure to give California driver's licenses to illegal residents are running out of patience and time.

Immigrant groups turned up the heat on Gov. Arnold Schwarzenegger Monday, marching at the state Capitol and accusing the governor of dragging his feet on a promise to support a driver's license bill for non-citizens.

"We do want what everybody who comes to America (wants), like you did, governor," said Sen. Gil Cedillo, D-Los Angeles.

Cedillo was the author of a law that granted illegal immigrants a California driver's license. The law was signed last year by former Gov. Gray Davis, but it was repealed. Now Cedillo says it's time for Schwarzenegger to agree on a replacement bill.

"We have a bill that strengthens national security, strengthens highway and community safety, and promotes citizenship. Now is the time for him to do this, and do so in a nondiscriminatory way," Cedillo said.

"He (Schwarzenegger) wants to try and find a solution to this, but he has very serious concerns about homeland security," said Schwarzenegger spokesman Vince Solitto.

Schwarzenegger is said to be looking at a proposal that would provide ID cards with a mark differing from a regular license, but he's facing strong opposition from members of his own party.

"In my opinion, it's not solvable. I think they shouldn't be here in the first place, and we shouldn't be giving them any form of driver's license," said Senate Republican leader Dick Ackerman.

"They are in this country in violation of federal immigration laws. Federal law requires they be deported. It's that simple," said Sen. Tom McClintock, R-Thousand Oaks.

But supporters of the bill say it's not that simple because California's economy is tied to jobs that are held by illegal residents. Peter Camejo, who is Ralph Nader's running mate on the Independent presidential ticket, says Schwarzenegger should do "the right thing."

"I think Arnold would actually gain politically. Because what I think it would show is, he's thinking independently. And when he makes a deal, he keeps his side of it," Camejo said.

If a deal isn't struck by the end of the month, it will be dead for the year. Cedillo says he's still focusing on getting an agreement with the governor before seeking a vote in the Legislature. But the current session ends on Aug. 31.