After days of blistering criticism from Illinois Rep. Luis Gutierrez, both the White House and Congressional Hispanic Caucus leadership pushed back yesterday on immigration reform, insisting the process is moving along. White House spokesperson Bill Burton told Roll Call that the administration is still working on a bipartisan bill and expects immigration reform “will be addressed very soon.”

The statement came after Wall Street Journal reported President Obama called Massachusetts Republican Sen. Scott Brown yesterday to lobby for his support on a bipartisan bill, presumably the enforcement-heavy bill Sens. Charles Schumer and Lindsey Graham have been working on for months. Graham has said health care reform soured him on working with Democrats on immigration. Majority Leader Harry Reid, who’s failing reelection campaign has prompted him to thrash around on the topic, told local reporters that Democrats need to look beyond Graham to moderate Republicans like Brown. But WSJ’s report doesn’t make Obama’s outreach sound promising:

“He called me originally about illegal immigration, something that he wanted me to look at that was coming down the pike,” Brown says of the call, which also roamed onto other topics like basketball and financial regulation. “I told him and others that I will read anything and make a judgment when it comes forth.”

Alluding to the issue a few minutes later, Brown clarified what he told Obama. “When I said I have an open mind, it means I have an open mind to read the bill,” he said. “That doesn’t mean that I will vote for granting amnesty to anyone. But I want to be respectful to the president and to any member who brings me a proposal.”

Meanwhile, Congressional Hispanic Caucus leadership has rushed to the Democrats’ defense.

CHC Chair Rep. Nydia Velazquez told Roll Call, “I think the president understands the importance of this issue not only from a human perspective, but also its fundamental importance to the Latino community.” Vice chair Rep. Charlie Gonzalez insisted Obama has “kept his word” and that political realities — presumably the Democrats’ loss of a 60th vote — mean “the lift has been made a little heavier for everyone.”

Gutierrez has argued loudly in recent days that Obama is ignoring his campaign vow to Latinos and has suggested that failure will drive Latino voters to “refuse to participate” in the November elections.

Meanwhile, Graham’s cold feet on a bipartisan bill haven’t kept him out of the far right’s line of fire. The rabidly anti-immigrant group Americans for Legal Immigration PAC (ALIPAC) has launched a campaign professing to out Graham as gay. In a speech to a Tea Party rally — which is making the web rounds via YouTube — the group’s leader, William Gheen, speculated that Graham’s being blackmailed into participating in immigration reform because of his “secret.” “I need to figure out why you’re trying to sell out your own countrymen and I need to make sure you being gay isn’t it,” Gheen said.

Seems the debate’s off to a civil start.