JACKSON HOLE, Wyoming (Reuters) - Republican Party grandees gathered in the shadow of Wyoming's majestic Grand Teton mountains on Thursday for a high-dollar fundraising event that added to presidential candidate Mitt Romney's brimming campaign coffers.

Hosted by former vice president and native son Dick Cheney, who often goes fly-fishing for trout in nearby streams, the country club reception and dinner brought in more than in $4 million for Romney, making it one of the biggest fundraising nights of the 2012 election season.

Business and party figures whooped and cheered for Romney at the reception in Jackson Hole, a rugged valley settled by beaver trappers in the 19th century that is now a playground for the rich. Visitors come for winter skiing and summer outings on the Snake River and a glimpse of bear, moose and elk.

Cheney, 71, looking well just months after heart transplant surgery, fired up the crowd gathered under a party tent set up on pristine grass near the golf range at Teton Pines Country Club. The crowd nibbled on hors d'oeuvre's such as prosciutto-wrapped shrimp and potstickers and sipped wine and beer as they listened.

"I have some strong feelings about what we need in a president, about how difficult the job is and the kind of challenges that a president has to deal with," said Cheney, a veteran of four Republican administrations. "Looking back and reflecting on that, I think there is only one man who â¦ meets those requirements, and that's Governor Mitt Romney."

The gathering was a stamp of approval for Romney from Cheney and the Republican establishment, which has long favored the former Massachusetts governor as the party's best chance to defeat President Barack Obama.

"I think it's a strong endorsement for Romney by a very visible conservative figure in the Republican Party, and I think that's a big plus for Romney that will help the enthusiasm of a lot of people on the conservative side," said John Bolton, who served the Bush-Cheney administration as U.S. ambassador to the United Nations.

Though the men are not close, Romney and Cheney are united in their belief that Obama must be defeated. Many of Romney's foreign policy positions have been cheered by "neo-conservatives" associated with Cheney.

Taking the microphone as Cheney sat alongside him, Romney went through a litany of complaints about Obama, chiefly on the weak state of the U.S. economy.

"I think they're wondering why in the White House, why has it gone so wrong," said Romney. "And the answer is they tried to put in place liberal economic policies and liberal policies don't work."

It was red-meat rhetoric for the gathering of Republican donors who paid either $1,000 to attend the reception, $10,000 for a photo with Romney, or $30,000 to have dinner with him at Cheney's house, the first time Cheney had opened his home here for a political fundraiser.

Jackson Hole resident John McQuillan, who had camped in the Tetons at the 9,500-foot level on Wednesday night for recreation, came down out of the mountains to attend the event.

"I'm a hard-right, Tea Party guy," said McQuillan, who said of Romney, "He's conservative enough for me."

Jackson Hole's rustic chic is reflected in its faux Wild West theme. The area combines fancy, ranch-style spa resorts with tourist attractions like a huge pile of elk antlers stacked into an arch in Jackson's main square.

The Million Dollar Cowboy bar, featuring bar stools made out of horse saddles, is a popular draw. Buildings are done up with a log-cabin veneer, from Ace Hardware to the stores at Powder Horn Mall. Rising in the distance are the Tetons themselves, which top about 14,000 feet.

CHENEY EMERGES

The hawkish Cheney had emerged from seclusion in April after receiving a new heart to call Obama an "unmitigated disaster" and declare that Romney is doing a "whale of a job."

While popular among conservatives, Cheney is a polarizing figure for many Americans. He was a strong proponent of the unpopular Iraq war launched by President George W. Bush and pushed the use of controversial interrogation techniques for terrorism suspects after the September 11, 2001, attacks.

The dinner, with about 200 guests, was co-hosted by Dick Scarlett, chairman and chief executive of United Bancorporation of Wyoming, and his wife Maggie, and Allan Tessler, former chief executive of Data Broadcasting Corporation, and his wife Frances.

Cheney's house adjoins the 18th green of the country club golf course and the meal took place under a tent there with golf carts parked under a trees.

Cheney noted that he and Scarlett go hunting.

"Dick's a man of great courage and I know that, because he hunts with me," said Cheney, who once accidentally shot and wounded a friend in Texas while bird hunting.

The Wyoming gathering brought Romney's two-day fundraising haul to about $5.5 million after a $1.5 million fundraiser on Wednesday in Montana. This is on top of the $106 million he and Republicans raised in June, a figure that far outpaced Obama's total of $71 million for the month.

In spite of Romney's fundraising prowess, he faces major challenges in defeating the seemingly nimble Obama campaign, which has been attacking him over his past as a private-equity executive and demanding he release more information about his personal wealth to try to keep him off balance.

Larry Sabato, a political science professor at the University of Virginia, said appearing with Cheney could create an awkward image for Romney with the broader voting public.

"There are certainly more popular politicians that Romney could choose to associate himself with," he said. "But the assumption is that $4 million is worth one bad headline in July."