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(Changes third bullet to show Romney clinching nomination)
* Obama campaign: Romney "lacks backbone" to stand up to Trump
* Romney: "I don't agree with all the people who support me"
* Romney clinches nomination with Texas primary
By Sam Youngman
LAS VEGAS, Nev., May 29 (Reuters) - Controversy over the "birther" movement hung over a meeting in Las Vegas on Tuesday between Mitt Romney and high-profile supporter Donald Trump, whose comments about President Barack Obama have put the Republican presidential candidate in an awkward spot.
Trump has again raised doubts about whether Obama was born in the United States, an issue that is most passionately pursued by conspiracy theorists and which Romney has tried to avoid as he focuses on attacking the White House's economy record.
"A lot of people are questioning his birth certificate," Trump said on CNBC on Tuesday. "They're questioning the authenticity of his birth certificate.
"I've been known as being a very smart guy for a long time. I don't consider myself birther or not birther but there are some major questions here and the press doesn't want to cover it," he said.
Romney has said he believes Obama was born in the United States but he has drawn fire from Democrats for not distancing himself from Trump, who has alleged Obama was born in Kenya and is thus not eligible to be U.S. president.
Romney later appeared with Trump, who once had presidential ambitions of his own, at a fundraiser in Las Vegas. But Trump avoided the issue altogether when introducing Romney at Trump International Hotel.
Romney clinched the Republican nomination on Tuesday night in the Texas primary, where he picked up scores of delegates and reached the target of 1,144 needed.
Trump congratulated Romney telling the 200 people who paid as much as $50,000 to attend that Romney would "make an absolutely great president."
The Obama campaign took aim at the Romney-Trump pairing by releasing a video "highlighting Mitt Romney's failure to condemn Donald Trump's over-the-line rhetoric."
"If Mitt Romney lacks the backbone to stand up to a charlatan like Donald Trump because he's so concerned about lining his campaign's pockets," the Obama campaign said in a statement, "what does that say about the kind of president he would be?"
Romney declined to condemn Trump in remarks to journalists on his plane on Monday.
"You know, I don't agree with all the people who support me," Romney said. "My guess is they don't agree with everything I believe in. But I need to get 50.1 percent or more and I'm appreciative to have the help of a lot of good people."
Trump had pushed the birth certificate issue last year and said he was at least partly responsible when the White House released Obama's long-form birth certificate from a hospital in Hawaii in hopes of ending the discussion.
In addition to the fundraiser with Trump and former Republican rival Newt Gingrich, which is expected to raise about $2 million, Romney also met with casino owner Sheldon Adelson, the multimillionaire who along with donations from his family kept Gingrich's campaign afloat for months with donations to Gingrich's "Super PAC" of more than $20 million.
Romney and Adelson met at Adelson's Venetian Hotel.
After trailing Obama in the fundraising stakes for many months, Romney raised almost as much money in April as his opponent. The former Massachusetts governor took in more than $40.1 million in fundraising efforts for his campaign and the Republican National Committee. (Editing by Bill Trott and Christopher Wilson)