A disconnect is growing among Hispanic lawmakers over the strategy for moving comprehensive immigration reform, with some pressuring President Barack Obama to push legislation this summer and others acknowledging the issue likely will have to wait until after the midterm elections.

Some leading voices in the Congressional Hispanic Caucus are becoming increasingly aggressive in their calls for Obama to demand immigration legislation this year.

The president needs to “put his back into the push for comprehensive immigration reform,” Rep. Luis Gutierrez (D-Ill.), who chairs the CHC’s Immigration Task Force, said Tuesday. Specifically, he called on Obama to help round up the necessary votes to pass Senate legislation during the work period between Memorial Day and the Fourth of July.

“The president needs to begin to work harder and bring the people together so that we can get this process started in the Senate, and it must begin immediately,” Gutierrez said.

Gutierrez went so far as to say he is holding open the possibility of urging Hispanic voters to stay home on Election Day if the White House and Congressional leaders don’t do enough to try to advance immigration reform in the coming months.

“Will I rule it out in the future? Absolutely not,” he said. If nothing else, Hispanic voters “can simply stay home, and that, to me, seems to be an option that is there” even without lawmakers’ urging, he added.

Gutierrez’s comments are the latest flash of discontent within the Hispanic community over Obama’s lack of action on their priority issue. Earlier this month, Democratic Caucus Vice Chairman Xavier Becerra (Calif.) said in a radio interview that Latinos view Obama with “suspicion” and question his priorities since he failed to follow through with a pledge to pass immigration reform in his first year in office.

“The president made a promise,” Becerra said during the interview. “He hasn’t fulfilled that promise.”

But as some Hispanic lawmakers up the ante on Obama, other CHC leaders say election-year pressures might make action on reform an impossible task this year given GOP opposition and a shrinking window of time for legislative action.

CHC Vice Chairman Charlie Gonzalez (D-Texas) said Obama has “kept his word” on helping to advance immigration reform simply by keeping it on his radar screen and mentioning it in key speeches, such as the State of the Union.

The “reality on the ground” is that it may not happen this year, Gonzalez said. “Immigration, like any other issue, takes serious debate. … We’re not quitting. It’s just that the lift has been made a little heavier for everyone” because of election season.

Gonzalez said CHC members have already begun compiling a list of key lawmakers for Obama to target after the November elections. “The president obviously is very persuasive,” he added.

Similarly, CHC Chairwoman Nydia Velázquez (D-N.Y.) defended Obama’s commitment to getting something done and said Hispanic lawmakers “continue to have productive discussions” with him.

“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,” Velázquez said.

The president has stepped up his role on the issue in recent weeks amid growing criticism from immigration rights advocates, who last month organized more than 200,000 people to rally in Washington, D.C., to call for action on immigration reform. Days before the rally, Obama held a series of hastily called meetings with activists and key lawmakers that resulted in his promise to press for Senate action on comprehensive reform this year.

“This is an issue that is very important to the president. It’s something that I know that the Senate Majority Leader has said is going to see action this year. And we’re obviously in consultation with both Republicans and Democrats to find a bipartisan solution to what is a very large problem and one that we think will be addressed very soon,” White House Deputy Press Secretary Bill Burton said Tuesday.

The president has already begun reaching out to Senators who could play a key role in advancing a bipartisan reform package; Burton said Obama called Republican Sen. Scott Brown (Mass.) from Air Force One on Tuesday to discuss the issue.

Brown spokeswoman Gail Gitcho said the Senator told the president “that he would review any legislation if it came before the Senate” but that for now his focus is on “fixing the economy and creating jobs.”

Gutierrez said he spoke with Senate Majority Leader Harry Reid (D-Nev.) on Tuesday and pledged to “be as helpful and supportive as possible” of Senate efforts to pass immigration reform this summer. He said he has “a lot of confidence” in Reid’s commitment to moving an immigration bill this year and predicted GOP support would materialize once a bill is on the table.

In an interview with local media outlets Monday, Reid acknowledged the difficulties that Democrats have had in reaching a deal on a final package with Sen. Lindsey Graham (S.C.), the leading Senate GOP proponent of immigration reform. He said he and other leaders need to reach out to other moderate Republicans such as Brown and Maine Sens. Susan Collins and Olympia Snowe.

Democrats need to “not put all of our eggs in one basket” by counting on Graham as the only Republican supporter, Reid said, according to the Spanish-language newspaper La Opinión.

But at this point, it does not appear Reid has begun that effort. Brown said he hasn’t been contacted by Reid or any other Democrats besides Obama seeking his support for an immigration reform proposal.

“I haven’t had any discussions on it in the last couple of months,” Brown said.

Immigration reform advocates say Obama has to do more to win over Latino voters in the coming months, particularly given the way the health care debate played out. During that debate, Hispanic lawmakers reluctantly accepted language in the bill on restrictions for legal and illegal immigrants that they found objectionable. Now, some feel it is time for Obama to use his political capital to help pass their priority issue since they helped him pass his top issue.

“The truth of the matter is that we know that there are voters, Latino voters, who supported the Obama administration in 2008 who are extraordinarily disappointed with the fact that comprehensive immigration reform has not moved,” said Thomas Saenz, president of the Mexican American Legal Defense and Education Fund.

“A natural result of that disappointment is that some of them, perhaps many of them, perhaps a significant portion of them, will not make the effort to support him in this election,” Saenz said.

John Stanton contributed to this report.