Sen. Lindsey Graham (R-S.C.) predicted Tuesday that a new Arizona law cracking down on illegal immigration would have a hard time surviving a court challenge from the Obama administration or another opponent.

“I think it’s going to meet a lot of headwinds,” Graham said, although he noted that he was not a constitutional lawyer. “I think it’s going to get challenged. My belief is it’s going to be tough … I don’t know where the courts will come out, but I think it will be a tough challenge for the law.”

Graham had been working with Sen. Charles Schumer (D-N.Y.) to negotiate an immigration bill, but in light of recent indications from Majority Leader Harry Reid (D-Nev.) that there might be an effort to pass a bill this summer, he has now said he wants assurances that no bill will come to the floor this year. Graham wants a climate change bill to move first, and immigration reform to wait until next year.

The Arizona law, which would make it a crime to be in the country illegally and require anyone suspected of being an illegal immigrant to show identification, has injected new momentum into calls for comprehensive immigration reform. The Arizona law has been roundly criticized by Latino groups, the Obama administration and top Congressional Democrats.

Attorney General Eric Holder told reporters Tuesday that the Obama administration was considering — among other responses — a court challenge to the “unfortunate” law.

White House spokesman Nicholas Shapiro said the Arizona law threatens to undermine “basic notions of fairness,” adding that Obama “has instructed members of the administration to closely monitor the situation and examine the civil rights and other implications of this legislation.”

“We believe that if we continue to fail to act at a federal level, we will continue to see misguided efforts opening up around the country,” Shapiro added.

Schumer, chairman of the Judiciary Subcommittee on Immigration, Refugees and Border Security, declined to comment Tuesday on the constitutionality of the a Arizona law or the prospect of a court challenge by the Obama administration.

Majority Leader Harry Reid (D-Nev.) said he had heard a challenge from the Obama administration was possible, but that he did not know whether a the law would survive a legal challenge.

Several Judiciary Committee Republicans said they thought courts could decide the law was constitutional.

“My sense is that it’s not a whole lot different from the current law with regard to what federal law enforcement authorities can do,” said National Republican Senatorial Committee Chairman John Cornyn (Texas), a former judge.

But Cornyn noted that he had not examined the law closely, as did Sen. Jeff Sessions (Ala.), the ranking member on the Judiciary Committee.

But Sessions indicated the Arizona law might be a step in the right direction, given that it empowers local law enforcement.

“I have long believed that we have wrongly excluded local law enforcement from virtually any role in immigration,” Session said.

Sen. Scott Brown (R-Mass.), meanwhile, took a shot at the Obama administration for being critical of Arizona, saying the administration has not done enough to secure the border.

“I’m not sure why the administration is throwing stones at the legislature and governor in Arizona, for example, when they should be working together to solve the problems and address the very, very real concerns that the citizens of Arizona have,” said Brown, who Obama personally called from Air Force One last week to discuss immigration.

“I know that they have asked for many years for assistance from the federal government, and obviously, what they did is a sign of frustration at not having help addressing these things.”

Rep. Joe Baca (D-Calif.) is among the Congressional Hispanic Caucus members urging a boycott of Arizona because of the new law. But Baca said the Arizona law did have a silver lining in that it provided an impetus to restart the debate over comprehensive immigration reform.

“I think the law in Arizona probably got people to think about the system that’s broken and the need for comprehensive immigration reform … whether it’s taken before climate change or any other legislation. Leadership will determine when it’s appropriate to take it up, but I think what happened in Arizona …. stimulated action on the Senate side.”