WASHINGTON (AP) — After Mitt Romney's loss in the presidential election, Republicans quickly identified one of their mistakes as the party's dysfunctional relationship with Hispanic voters, who overwhelmingly voted for President Barack Obama. But the earliest efforts by GOP lawmakers to tackle immigration policy on Capitol Hill aren't likely to win them new support among Hispanics.

The first immigration-related bills offered by Republicans this week would provide legal status for hundreds of thousands of young immigrants — but no way for them to become U.S. citizens — and would eliminate the popular diversity lottery that randomly awards green cards to would-be immigrants from countries with low rates of immigration to the United States. The two bills have virtually no chance in the lame-duck session, but they are significant because they are the first on the legislative agenda since the election.

Early reviews aren't enthusiastic.

"We don't see the writing on the wall," said Lionel Sosa, a Texas Republican who served as a Hispanic media consultant for presidents Ronald Reagan, George H.W. Bush and George W. Bush. "We don't see that the electorate is changing and we need to make changes. The longer we send out messages that Latinos take some offense to, the longer it's going got take us to recover the Latino vote."

Republicans are offering some olive branches to Hispanic voters. Retiring Republican Sens. Jon Kyl of Arizona and Kay Bailey Hutchison of Texas introduced on Tuesday a narrowly tailored DREAM Act-like bill dubbed the Achieve Act. It offers visas for some young illegal immigrants who arrived before they turned 14 and are 28 or younger and are in the military or pursuing a college or technical degree, but it wouldn't allow them any way to become citizens.

The DREAM Act, which narrowly passed the House before being defeated in the Senate two years ago, would offer citizenship for young illegal immigrants. Such proposals have been derided as "amnesty" by GOP lawmakers — and by Romney, who promised he would veto the legislation.

This week, House Republicans are also considering a bill that annually would give 55,000 new green cards, or permanent visas, to foreign students in science, technology, engineering and math. The so-called STEM bill would also make it easier for those green card holders to be reunited with spouses or children living abroad. But it would eliminate the popular diversity lottery, and Democrats have argued that it actually would reduce overall legal immigration.

Kyl, one of the bill's sponsors, said the timing of the legislation isn't a political response to the election.

"We have to get the ball rolling," he said.

Romney's chief political strategist this week said the campaign's biggest mistake was how it dealt with Hispanic voters. "We should have done a better job reach out to Hispanic voters," Stuart Stevens said in an interview with CBS's Charlie Rose on Thursday. "We should have done it earlier and in a more effective way." One day earlier, in an op-ed published in the Washington Post, Stevens noted that Romney did better than Obama among what he described as middle-class voters, especially white voters younger than 30, and described Obama's strategy as "being too liberal and too dependent on minorities."

Democratic lawmakers said their political opponents are missing a chance for bipartisan support on the STEM bill by adding conditions such as ending the diversity lottery.

"That's not the way we are going to achieve success," said Sen. Bob Menendez, D-N.J. "There was a deal on the table, it could have been a good step forward."

Rep. Luis Gutierrez, D-Ill., said: "It's almost as though they didn't hear the call from voters on Election Day on Nov. 6."

Sosa, who has made a living appealing to Hispanic and Latino voters for Republican candidates, said the Republican efforts should at least be considered a step in the right direction. But he warned that the party has to move to center on immigration.

"We need to quit making offensive gestures to the Latino community," Sosa said. "Wanting to oppose the DREAM Act, in my opinion is totally ridiculous."