AUSTIN — The clock is starting to run out on contentious immigration legislation offered this year by tea party Republicans in the Legislature.

With five weeks left in lawmakers’ session, hard-line measures — including bills on college tuition for those in the U.S. illegally and on “sanctuary city” policies — are languishing in the Senate and lacking traction in the House.

But the prospect that those efforts could fade away with a whimper doesn’t mean they’ve lost their emotional punch. If anything, the impasse highlights a simmering divide in the GOP.

Some Republicans, hoping to boost outreach to Hispanic voters, view the measures as unnecessary and needlessly inflammatory. Others, responding to the GOP’s conservative base, see an all-out response to illegal immigration as a key part of border security.

With lawmakers still needing to sort out the particulars on tax cuts, transportation funding and other significant legislation, some Republicans would rather avoid a disruptive immigration clash.

“We just don’t have the time in 140 days to deal with the big-ticket issues and also pander to a small percentage of movement conservatives,” said Rep. Jason Villalba, R-Dallas.

The tension over immigration policy comes even though Republicans are mostly in lockstep on the need to enhance enforcement along the Texas-Mexico border.

Republican lawmakers of all stripes cite a perceived federal government failure to secure the border as the prime reason Texas has been forced to step in. The House and Senate have passed far-reaching and largely similar border security bills.

Both would boost spending on border security to well over half a billion dollars over the next two years — though the Senate wants to spend hundreds of millions more, largely to extend the presence of the National Guard.

But the GOP splits from there, with some hard-liners accusing more moderate Republicans, especially in the House, of only paying lip service to the issue. Policies such as the tuition change are needed, they argue, to deter illegal crossings.

“The House wants the talking point of addressing illegal immigration without actually passing the substantive policy that would address it,” said Luke Macias, a Republican consultant whose clients include several tea party lawmakers.

Senate measures

In the Senate — presided over by GOP Lt. Gov. Dan Patrick, who campaigned last year on cracking down on illegal immigration — committees have approved a few immigration proposals.

One would repeal the longstanding law that allows some students who are in the country illegally to pay college tuition at lower, in-state rates. Another would bar local rules that prohibit police from asking the immigration status of people they stop — the sanctuary cities policies.

A third seeks to allow Texas and other states to enforce federal immigration laws — and to perhaps create their own dedicated border security force.

Supporters argue that the federal government’s immigration approach has forced their hands. They’ve also expressed a desire to eliminate “magnets,” policies that they say create an incentive for more people to enter the country illegally.

“It’s just bad policy that rewards illegal immigration in perpetuity,” Sen. Donna Campbell, R-New Braunfels, said this month, explaining why she wrote the bill to repeal the in-state tuition program.

The sanctuary cities bill and in-state tuition measure are stalled in the Senate, where it appears they might lack the 60 percent support — 19 of the 31 members — to be brought up for debate.

And it’s unclear how much support exists for the interstate border security compact idea.

But that’s still more traction than has been gained in the House, run by GOP Speaker Joe Straus.

House resistance

Similar bills there haven’t received a hearing, much less a vote, in the State Affairs Committee. And the panel’s chairman, Rep. Byron Cook, R-Corsicana, has expressed unease with such legislation, particularly the tuition measure.

“I would just hope that we take a more measured, more common-sense approach,” he said.

So while Democrats have led the charge against such measures — rallying passionate opposition that has included young people visiting the Capitol to argue their case — Cook’s quieter resistance highlights that some Republicans also continue to push back.

Those who want to keep the tuition break for some who are in the country illegally say repealing it would harm promising students who just want to contribute to society. And many law enforcement officials have warned that the sanctuary cities bill would stretch local resources and hurt community policing efforts.

“It doesn’t serve any purpose,” said Sen. Kevin Eltife, a Tyler Republican who pledged to help block such legislation in the Senate. “And it goes against the grain, when we are trying to include Hispanics in the Republican Party.”

Texas Republicans have had more success than their counterparts elsewhere in the U.S. in reaching out to Hispanics, the state’s fastest-growing population group.

Wooing Hispanics

A Gallup poll last year showed that 27 percent of Hispanics in Texas call themselves Republicans, compared with 21 percent in the rest of the country. And exit polls, disputed by some Democrats, showed that Republican Greg Abbott garnered 44 percent of the Hispanic vote in winning last year’s gubernatorial election.

Experts said efforts such as the in-state tuition program — passed in 2001 with overwhelming bipartisan support — have helped the GOP make inroads with Latinos. And a more welcoming tone by Abbott and others could further the party’s appeal to the demographic group.

A continued focus on divisive immigration proposals, however, could roll back the gains, experts said.

“Democratic leaders fall on their knees every night and pray, ‘Dear God, please let them keep talking about taking away the in-state tuition,’” said Jerry Polinard, a political scientist at the University of Texas-Pan American, in Edinburg.

GOP backers of the more contentious immigration legislation dispute that they’re harming their party.

Rule of law

Hopeful that their proposals still have a chance, they counter that true conservatives ultimately respect efforts to shore up the rule of law. And those lawmakers, such as Rep. Pat Fallon, R-Frisco, said they are simply representing the concerns of their constituents.

“I’ve knocked on probably 15,000 Republican primary doors … and I’ve never heard one of them say, ‘We don’t like immigration,’” said Fallon, who offered one of the bills to stop the in-state tuition program. “Nobody is saying that. They just want it done legally.”

Follow Tom Benning on Twitter at @tombenning.

AT A GLANCE: WHERE 3 KEY MEASURES STAND

  1. Repeal of tuition law: Seeks to change the 2001 law that allows some students who are in the country illegally to pay college tuition at in-state rates.

Status: Out of Senate committee. May not have enough votes to be heard on Senate floor. No House committee hearing scheduled.

  1.  “Sanctuary cities” bill: Would bar local rules that prohibit police from asking the immigration status of people they stop.

Status: Out of Senate committee. May not have enough votes to be heard on Senate floor. No House committee hearing scheduled.

  1. Interstate border security compact: Would potentially allow Texas and other states to enforce federal immigration laws — and perhaps to create their own border security force.

Status: Out of Senate committee. Prospects in full Senate unclear. No House committee hearing scheduled.