AUSTIN, Texas — Barack Obama has erased George W. Bush’s inroads among Hispanics, with these influential voters consistently giving the president exceptionally strong marks and the White House employing an aggressive strategy to keep it that way.

Obama’s challenge is to ensure that Hispanics pledge allegiance to the Democratic Party for the 2010 elections and keep supporting him through his own likely 2012 re-election race while he tackles the divisive issue of repairing the nation’s patchy immigration system.

Hispanics are the nation’s fastest-growing minority group. The government projects they will account for 30 percent of the population by 2050, doubling in size from today and boosting their political power.

If Democrats build on Obama’s gains, Texas and other traditionally Republican states with huge numbers of Hispanics could be within reach in the future. That would mean deep trouble for a GOP that’s already older, whiter, dwindling in numbers and lacking a standard bearer to make Hispanics a priority the way Bush did.

Yet while the latest Associated Press-GfK poll showed that a strong 68 percent of Hispanics approve of the job Obama’s doing, maintaining such support is far from certain.

“Democrats speak to me, and this one in particular seems to be listening to what we need and what we want,” said Tina Calhoun, 52, of Sacramento, Calif., who grew up in a family of Republicans but tends to vote Democratic. Still, she, like many others, isn’t necessarily going to stick with Obama no matter what. “I want to give him a little more time,” she said.Indeed, it’s unclear whether Hispanics will back Democrats to such strong degrees next fall when Obama is not on the ballot. Minorities and young voters who turned out in droves for Obama in 2008 didn’t show up this year for Democrats in the Virginia and New Jersey governors’ races.

There’s also a lifetime before Obama’s expected re-election campaign, and he’s promised to push immigration legislation before then, including an eventual path to citizenship for some 12 million people in the country illegally.

That’s no easy task. The spectacular failure of such a measure in 2007 proved as much.Immigration is a galvanizing issue on both the left and the right, with pitfalls for both parties. Republicans could alienate Hispanics if the vocal right again takes control of the debate with angry rhetoric.

Democrats risk seriously disillusioning Hispanics by inaction, delay or a piecemeal approach. A fight in Congress is assured.

“Our community will judge him based on how he delivers on the promise he made to see immigration reform early in his administration,” said Janet Murguia, president of the National Council of La Raza, suggesting the issue trumps everything else.

Much was made during the Democratic primary of Obama’s perceived weakness among Hispanics but he won 67 percent of their vote in the general election to 31 percent for Republican John McCain. It was a huge jump from 2004 when Democratic nominee John Kerry won Hispanics by 53 percent to 44 percent for Bush, a Texan who focused heavily on Hispanics.

Obama didn’t win Texas, hard-core GOP country for decades. But 20 percent of voters here were Hispanic, and, of those, Obama won 63 percent of their vote.

Obama dominated counties that include Austin, Dallas, Houston and San Antonio, where huge numbers of Hispanics live, as well as heavily Hispanic counties along the Mexican border, where he increased Kerry’s margins by double-digits — a warning sign for Republicans.

Overall, the president has watched his job approval rating steadily decline since January; it stands at 54 percent in the latest AP-GfK poll. His support among Hispanics has largely held steady, with some surveys finding his backing among them as high as the low 70s — a figure even Republicans call impressive.

“They flirted with Republicans because they liked Bush. But the whole immigration fight really reversed all the gains Republicans had made,” said Andrew Kohut, a nonpartisan pollster at the Pew Research Center. “There’s no question that they are part of the Democratic base now.”

Since Day 1, the White House has made a concerted daily effort to court Hispanics.Obama chose Ken Salazar and Hilda Solis for his Cabinet, and then nominated Sonia Sotomayor for the Supreme Court as part of what officials call a record number of Hispanic appointments.

The president and administration officials have given numerous interviews to Hispanic media.

The White House held the first known bilingual White House press briefing. It also partnered with Univision and Telemundo to broadcast White House events. And it has made several Web sites available in Spanish, including WhiteHouse.gov.

All of that has struck a chord with Lucy R. Moreno of Houston, 70.

“Finally, we’re getting what’s due to us. I’m pleased that he’s following through on what he said he would do, like put Hispanics in positions of power,” she said. “And he’s hitting the right issues.”

Mel Martinez, a Republican and former Florida senator, attributes Obama’s standing among Hispanics both to his personal popularity as well as the GOP’s failure to build upon Bush’s gains in a serious way.

“It’s a shame and it’s something we’re going to regret,” he said. “To be a majority party, you must be focused on Hispanics.”

• The Associated Press