Updated: 2:38 p.m.

In the latest sign of Hispanic lawmakers’ discontent with President Barack Obama, a House Democrat from Obama’s home state called Tuesday for the president to “put his back into the push for comprehensive immigration reform.”

Rep. Luis Gutierrez (D-Ill.), chairman of the Congressional Hispanic Caucus’ immigration task force, also laid out a timetable for Senate action on legislation that he said he had discussed as recently as Tuesday with Majority Leader Harry Reid (D-Nev.).

“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 said he spoke with Reid on Tuesday morning and pledged to the Majority Leader that he would “be as helpful and supportive as possible” of Senate efforts to pass the legislation during a timetable that Reid laid out.

“We have, according to Majority Leader Sen. Reid, a window, and that window is between Memorial Day and the Fourth of July,” Gutierrez said. “We need to begin to get the bill marked up.”

Gutierrez predicted that the Senate Judiciary Committee and floor schedule in that chamber would become tied up after the July Fourth recess with an attempt to confirm retiring Supreme Court justice John Paul Stevens’ replacement, so he called on Sens. Charles Schumer (D-N.Y.) and Lindsey Graham (R-S.C.) to introduce a bill right away.

“We love the outline that they suggested to us,” Gutierrez said. “We’d like them to fill it in so that we can begin to work and to add and to make sure that a bill comes forward out of the Senate so we can work here in the House,” Gutierrez said.

Although he said he is not actively seeking a meeting at the White House, Gutierrez said such an invitation could provide “a way to coalesce and move forward” on the issue

In the absence of Congressional action on a comprehensive bill this year, Gutierrez said he would continue to stress to fellow Democrats — including Obama — that Hispanic voters would have the “option” to sit out the midterm elections in November.

“They don’t necessarily have to fill the ranks of the Democratic Party,” he said. “They can simply stay home, and that, to me, seems to be an option that is there.”

Gutierrez added that he had not ruled out urging Hispanic voters to stay home on Election Day if he is not satisfied with White House and Congressional efforts to pass an immigration bill.

Both Gutierrez and Rep. Raúl Grijalva (D-Ariz.) called on Arizona Gov. Jan Brewer (R) to veto a bill that would dramatically toughen the state’s border enforcement efforts, and on Obama — if Brewer does not — to pre-empt Arizona’s ability to regulate the flow of people across the border.

Grijalva, who co-chairs the Congressional Progressive Caucus, also called on Obama to “move immigration reform — so that these kind of aberrations that are happening in Arizona on the issue of immigration do not become the standard operating policy for the rest of the country.”

Grijalva said also urged businesses and national organizations to boycott spending money in Arizona or doing business with the state and on the federal government to withhold money from the state.

The Hispanic lawmakers also took a swipe at the 2008 GOP presidential candidate, saying they were disappointed that Arizona Sen. John McCain — a lead Senate architect of the failed push for comprehensive immigration reform in 2007 — joined with Senate Minority Whip Jon Kyl (R-Ariz.) on Monday to introduce a 10-point proposal to crack down on the flow of illegal immigrants and drugs across the Arizona-Mexico border.

“It was a surprise to see him swing that far,” Grijalva said.

Reid and Speaker Nancy Pelosi (D-Calif.) have agreed that the Senate would act first on an immigration bill and both Reid and Majority Whip Dick Durbin (D-Ill.) recently have said they’d like to bring a bill to the floor this year. But McCain’s posture signals a tough road ahead in the Senate, given the realities of election-year politics.