What role will Obama play in immigration reform? It's not clear, yet.

President Barack Obama is treading carefully in deciding how visible a role he should play during perhaps the most delicate stage in the effort to overhaul U.S. immigration laws.

The Democratic president, having fought with conservatives in the Republican-controlled House of Representatives over everything from budget cuts and tax hikes to healthcare reform and environmental policy, is aware they are in no mood to compromise or to be lectured.

Obama has so far held back from major criticism of his political opponents even when it appears they could stall a central objective of his second term.

House Republicans are adamant against approving the Senate version of legislation and are instead talking about passing several bills that address various immigration problems, but not necessarily legalizing the estimated 11 million undocumented residents.

Unlike the public relations blitz that accompanied his healthcare law in 2010, Obama has made no sweeping travel plans to campaign for the legislation nor delivered any major speeches on the subject in the weeks since the Democratic-led Senate approved an immigration bill that he backed.

Instead, he has held meetings with groups like the Congressional Hispanic Caucus and sent out top economic adviser Gene Sperling and others to make the case publicly that legalizing the status of undocumented immigrants will prove an economic boon for the United States in the long run.

White House spokesman Jay Carney said Obama would make his case for the overhaul, but "how that manifests itself, what events he may hold, we'll have to see, because we're going to make those judgments as this issue ripens over the next weeks and months."

Obama on Thursday heard words of caution about his role from Senators John McCain, a Republican, and Charles Schumer, a Democrat, two members of the "Gang of Eight" senators who shepherded the Senate version. The two senators sat down with Obama at the White House.

McCain said afterward the challenge was to get recalcitrant House Republicans behind some form of immigration legislation and that it was important they not feel they were being unduly pressured by Obama.

"So I think the president is walking a careful line here and I think it's the appropriate thing," he said.

There is some skepticism at the White House that if Obama speaks out about immigration, it will drive away House Republicans, since many want to kill the legislation whether he talks about it or not.

One White House official said any presidential activity on the subject would be based on a calculation of whether it was needed and would be helpful.

We'll speak out, we'll travel, we'll do things with different decibels, depending on what we think will help move the ball," one White House official said.

'Got to let it simmer'

Obama is getting cautionary advice from other players in the immigration debate, such as Thomas Donohue, president of the Chamber of Commerce, which has been lobbying strongly for immigration reform.

Donohue said Obama needed to strike a balance on immigration reform and not try to rush House Republicans.

"He should be very careful not to get down into the weeds on this thing. He's got to let it simmer. He's got to let the House work its business," said Donohue.

Donohue and other supporters of reform said Obama's focus should be on boosting public support for an immigration overhaul. Supporters hope that if constituents in various lawmakers' districts voice their backing for the legislation, it could influence the debate in the House.

Obama has made passing an immigration overhaul a significant priority of his second term after giving the issue short shrift in his first four years because there was no political momentum for it in Congress and he was preoccupied with trying to get the U.S. economy going.

In the past when Obama has been faced with a high-profile debate in Washington, he has frequently argued his case to the voters in travels across the country, but with mixed success.

His high-decibel argument to persuade Republicans not to let $85 billion in automatic spending cuts take place last spring fell on deaf ears and the budget cuts went into effect.

Republican Representative Raul Labrador of Idaho, who served until recently on a working group on immigration and is open to a comprehensive bill, said Obama's effort to pass gun legislation this year was an example of why he did not think the president traveling to pitch immigration reform would help.

"All I remember is that the last time he traveled for a big issue, he killed it. He might actually want to rethink that," he said.

But there are many voices among Democrats who think a highly visible campaign would help pressure Republicans who saw overwhelming numbers of Hispanics vote for Obama's re-election over Republican challenger Mitt Romney last November.

"I think the president should be out there talking about it and pushing it, not just for political reasons," said Democratic strategist Bob Shrum. "He ought to be out there pushing this because someday it has to happen."

(Editing by Peter Cooney)