After an election that bared the GOP’s huge disadvantages on immigration, three influential Republican senators have introduced legislation that would grant legal residency to young people brought illegally to the United States, if they seek higher education or enlist in the military.

The proposal comes as more Republicans have called for the party to soften its opposition to illegal immigration in the wake of massive November electoral losses that were driven, in part, by low support among Latino voters.

The measure — sponsored by Sen. John McCain (Ariz.), and retiring Sens. Kay Bailey Hutchison (Tex.) and Jon Kyl (Ariz.) — would offer a Republican alternative to the so-called Dream Act, providing a pathway for young adults to apply for legal permanent residency — but not citizenship — if they have completed military service or higher education and have worked in the United States for at least four years.

Leading advocacy groups that push for immigration reform characterized the proposal as a half measure that would provide few new opportunities for normalization for young adults.

But Kyl said the measure is an effort to “get this ball rolling.”

A look at key factors in the 2012 presidential election.

“We have to have a discussion that is sensible, that is calm, that discusses all of the different aspects of the issue,” he said.

Despite Republican anxiety about the party’s inability to lure a growing number of Latino voters — President Obama beat GOP challenger Mitt Romney among Latinos by 44 percentage points — Hutchison and Kyl said their bill is not a response to the election.

Instead, they said it represents a year of behind-the-scenes work to come up with an alternative to the Dream Act that would let such young people remain in the United States without allowing them, as Kyl said, “to jump ahead of anybody in the citizenship path.”

Their voices, along with McCain’s, are particularly potent because they hail from Texas and Arizona, states with large and increasing immigrant populations.

The lawmakers said they are moving ahead with the legislation now so that it can receive a public airing before their Senate terms end this month. However, they said they are not optimistic about the measure’s chances in the lame-duck session, given the fiscal issues that will occupy most of lawmakers’ time in coming weeks.

And Sen. Richard J. Durbin (D-Ill.), the Senate’s lead driver of the Dream Act, said he wants Congress to use a growing consensus for action on immigration to take up a more far-reaching measure.

“We have some significant differences,” he said, noting that the Republicans did not discuss their measure with him before they introduced it. “But I appreciate their efforts to help.”

The bill, dubbed the Achieve Act, would extend a new visa to people younger than 28 who were brought to the United States before age 14. It would be available to those who do not have serious criminal records and who agree not to seek government benefits, including federal student loans.

The visa would allow young people to complete schooling or military service. They could then apply first for a work visa and, after four years, for a visa that allows permanent legal residency.

Although the lawmakers said they have had productive conversations with Sen. Marco Rubio (R-Fla.), who has been working on his own alternative to the Dream Act and has become a leading voice within the GOP on immigration reform, he indicated that he is soliciting input from stakeholders and is not ready to be a co-sponsor.

“The concept is the right one and it’s one that we helped them formulate,” he said. “We’re getting pretty close.”

The measure was also introduced without Democratic sponsors, despite calls from Democrats for Republicans to work on bipartisan immigration legislation.

Kyl — who held a joint news conference with Hutchison on Tuesday to announce the proposal — criticized Obama for his June decision to declare that his administration would stop seeking to deport those who would have qualified under the Dream Act.

“The administration has unfortunately chosen . . .to ignore current law because it didn’t think it was good policy,” Kyl said.

Clarissa Martinez de Castro, director of immigration and civic engagement for the National Council of La Raza, characterized the GOP proposal as a step backward, away from a growing consensus that young people brought to the United States as children should have access to citizenship.

“It seems more an attempt to pull negotiations away from the center,” she said.

Although some Republicans are likely to dismiss the proposal because it would offer amnesty to illegal immigrants, a senior Democratic aide, who is not authorized to speak publicly about pending legislation, suggested that the retiring Republicans should receive little credit for advancing the idea on the eve of their departures.

“It’s not exactly a profile in courage for two senators — who happen to turn into pumpkins in about a month — to weigh in on a bill that’s been around for a decade and that they’ve opposed for nearly as long,” he said. “It’ll be interesting to see if members of their party will be willing to continue the conversation they’ve waited far too long to start.”

Ed O’Keefe contributed to this report.