LAS VEGAS — Mitt Romney has won the Republican presidential nomination after years of fighting, though his triumph was partially overshadowed by the celebrity businessman who helped him along the way.

As primary voters in Texas on Tuesday pushed him past the 1,144-delegate threshold he needed to win the nod, Romney was raising money in Las Vegas with Donald Trump, the real estate mogul who has stoked doubts about whether President Barack Obama was born in America.

It’s the start of a weeklong push to raise millions of dollars during a West Coast swing as Romney looks to bring in as much cash as possible ahead of a ramped-up campaign schedule later this summer.

“Mr. Trump, thank you for letting us come to this beautiful hotel and being with so many friends. Thank you for twisting the arms that it takes to bring a fundraiser together,” Romney told the approximately 200 people who paid thousands to attend the event at the Trump International Hotel. “I appreciate your help.”

The Trump event and surrounding controversy overshadowed the Texas primary win that officially handed Romney the nomination, a triumph of endurance for a candidate who came up short four years ago and had to fight hard this year as voters flirted with a carousel of GOP rivals. According to the Associated Press count, Romney surpassed the 1,144 delegates needed to win the nomination by winning 105 delegates in the Texas primary, pushing his total to 1,191 delegates.

The former Massachusetts governor reached the nomination milestone with a steady message of concern about the U.S. economy, a campaign organization that dwarfed those of his GOP foes and a fundraising operation second only to that of Obama, his Democratic general election opponent. He outlasted a half-dozen Republican opponents to clinch the nomination later in the calendar than any recent GOP nominee.

Romney must now fire up conservatives who still doubt him while persuading swing voters that he can do a better job fixing the nation’s struggling economy than Obama. In Obama, he faces a well-funded candidate with a proven campaign team in an election that will be heavily influenced by the economy.

Romney will continue his push to raise money with fundraisers this week in wealthy California enclaves like Hillsborough, near San Francisco, and Beverly Hills. He has at least one major fundraising event every day for the rest of the week, as well as a series of smaller events.

But the focus Tuesday was on Trump, who once led polls of GOP primary voters. He endorsed the former Massachusetts governor just before the February Nevada caucuses, offering his support at a morning endorsement event in a ballroom in the hotel that bears his name. In the same room Tuesday night for the fundraiser, Trump introduced Romney. He steered clear of the “birther” issue as he spoke to donors, though just hours earlier he had repeated his doubts about the authenticity of the birth certificate that shows Obama was born in Hawaii.

“A lot of people do not think it was an authentic certificate,” Trump told CNN of Obama’s birth certificate. When CNN anchor Wolf Blitzer told Trump he was “beginning to sound a little ridiculous,” Trump responded, “I think you sound ridiculous.”

Such allegations about Obama’s birthplace have been repeatedly proven false. The state of Hawaii recently re-affirmed that he was born there.