A day after uttering a line that made him seem unsympathetic to the impoverished, Mitt Romney received the endorsement of perhaps the world's most self-satisfied rich man, Donald Trump.

The meeting between the pair, one of whom said recently he likes to have the ability to fire people if necessary, the other of whom has coined the reality-show slogan "You're fired!" took place Wednesday in a curtained-off area off the marble-and-chandeliered lobby of Trump International, Trump's posh hotel off the Las Vegas Strip. (There is no casino here.)

Trump came out from behind a blue curtain followed by Romney and his wife, Ann. Romney shook Trump's hand as he accepted the endorsement.

"Our country is in serious trouble," Trump said. "We really have an opportunity to do something great for the country.... It's my honor and privilege to endorse Mitt Romney. And by the way, this is a great couple," he said, looking at the Romneys, who speak often about their 42-year union.

"Mitt is tough, he's smart, he's sharp, he's not going to allow bad things to continue to happen to this country that we all love. So, Gov. Romney, go out and get 'em. You can do it."

Romney feigned a bit of surprise. 

"There are some things that you just can't imagine happening in your life," Romney said. "This is one of 'em. Being in Donald Trump's magnificent hotel and having his endorsement is a delight." He added that he is also seeking the endorsement of the people of Nevada.

Trump, Romney said, has shown "an extraordinary ability to understand how our economy works, to create jobs for the American people." Romney complimented Trump for his hard-line stance against the Chinese. "He is one of the few people who stood up and said, 'You know what? China has been cheating, they have taken jobs from Americans.'"

In comments to reporters before the formal endorsement, Trump, cotton candy hair aswirl on his crown, said he had gotten to know Romney better recently and likes his positions on China and OPEC.

It is unclear whether Trump's endorsement will help Romney, who is leading in the polls here in advance of Saturday's caucuses.

Trump has tried to be a player in this election, first declaring that he might compete for the nomination, perhaps as an independent if he didn't like the eventual GOP nominee, then taking a series of well-publicized meetings with candidates and potential candidates.

Last spring, on the eve of Romney's formal announcement that he was entering the race, Trump took Gov. Sarah Palin to dinner at a downscale pizza restaurant in Times Square.

Finally, in December, Trump said he would moderate a presidential debate in Des Moines. Only former House Speaker Newt Gingrich and former Pennsylvania Sen. Rick Santorum agreed to participate at a time when there were still seven candidates competing. The debate was cancelled.

Trump's endorsement can probably be seen more as an acknowledgement that Trump prefers a winner than that he feels a true connection to Romney, who he's often denigrated.

The Democratic National Committee, sensing an opportunity, immediately posted a video on YouTube highlighting some of Trump's attacks on Romney.

"Why would the Donald do that? Why would he endorse ... a man he's already mocked as someone who 'walked away with some money from a very good company he didn't create.' A man Trump has said has a history of 'eliminating jobs rather than creating them. A man he believes 'doesn't have a chance at the Republican nomination.' But Trump and Romney do have something in common. They both like firing people."

But the lack of respect has been mutual. When Trump tried to sponsor a GOP presidential debate, Romney said he was too busy to attend. "I spoke with Donald Trump," he said at the time, "and indicated that we just can't make his debate."

In his brief comments to reporters, Trump said he is a registered as an independent, but is considering changing his affiliation to Republican. He will not launch a third-party presidential bid if Romney becomes the nominee, he said, and believes Romney can beat President Obama.

"I think if he debates the way he's been debating, I think he'll beat Obama handily," Trump told reporters. "I think he can do great."

When asked about previous criticism of Romney, he acknowledged he'd had a recent change of heart.

"I never knew him, I knew of him and respected him, but I really got to know him over the last few months. I've had numerous meetings with him."

Trump said he'd been impressed by Romney's last pair of debate performances, which many pundits have said is responsible for his solid victory in Florida where he trounced former House Speaker Newt Gingrich.

"I thought he did really well, plus he's the one person that really speaks strongly about China. ... Because China is ripping this country like nobody is ripping this country, and he's the one person that continuously mentions China and OPEC. His position is very tough and it's what it should be."

Michael Mishak contributed to this report.