By Steve Holland

WASHINGTON (Reuters) - When Kevin McCarthy was struggling early this year to get enough votes from his own Republicans to become Speaker of the House of Representatives, Democratic President Joe Biden called the prolonged saga a national embarrassment, then had a little fun.

"I've got good news for you," Biden said, pointing playfully at a reporter after a speech in Kentucky. "They just elected you speaker."

During months of tense exchanges over the U.S. debt ceiling, McCarthy has also taken some swipes at Biden. Arguing that Biden should meet him to discuss his demands for lifting the debt ceiling in March, McCarthy made fun of the 80-year-old president's advanced age.

"I would bring lunch to the White House. I would make it soft food if that's what he wants. It doesn't matter. Whatever it takes to meet,” McCarthy told reporters.

In the last few weeks, however, both men have stopped the put-downs and cobbled together an agreement that will now lead to a congressional vote to suspend the U.S. debt ceiling and avoid a default that would wreak economic havoc on the country.

Like the deal they crafted, the relationship the two men forged does not look pretty but appears to have gotten the job done.

"I think he negotiated with me in good faith," Biden said of McCarthy on Sunday. "He kept his word. He said what he would do. He did what he said he would do."

The deal caps federal spending and forces more poor people to work for food aid, concessions that Democrats hate. But it also preserves much of Biden's Inflation Reduction Act and punts the next debt ceiling showdown into 2025, which Republicans hate.

STRANGE POLITICAL BEDFELLOWS

Biden, a veteran former senator from Delaware, talks about the days when both parties would often come together to solve pressing problems, and he has pushed his fellow Democrats to find across-the-aisle agreements as part of his larger attempts to re-center the country.

Although he initially called for the debt ceiling to be raised without negotiations, he ended up making compromises.

McCarthy, a 58-year-old Californian, is representative of a pugilistic style of Republican politics that took root with the "Tea Party" and blossomed under former President Donald Trump.

He came up through the party ranks pushing tax cuts for companies and reduced government spending and is now presiding over an unruly Republican Party in which radical lawmakers have threatened to force him out of the Speaker job unless he takes a hard line with the White House.

After an initial Feb. 1 meeting at the White House, an optimistic McCarthy predicted that he and Biden would find common ground and meet again soon.

Instead, a three-month stand-off ensued.

Biden refused to negotiate as the White House bet that investors and business groups would persuade Republicans to back off their threat to drive the United States into default.

Both McCarthy and Biden spent that time accusing the other of putting the U.S. economy at risk. McCarthy complained of his own isolation from the White House.

"I never had somebody from the White House reach out to me. Not one person from the administration called me. I called them," the House speaker told reporters at a Republican retreat in March.

Even after negotiations finally began in earnest, McCarthy portrayed the president as the captive of "socialists" intent on default.

"He'd rather be the first president in history to default on the debt than to risk upsetting the radical socialists who are calling the shots for Democrats right now," McCarthy tweeted last week.

But his tone changed as both sides moved toward a deal last week, expressing his respect for White House negotiators: "These are highly intelligent, highly respected on both sides. They know their work, they know their job, they know the numbers."

House Republican Patrick McHenry, a key negotiator in the talks, noted that Biden and McCarthy were "two Irish guys that don't drink" but had found a way to work together.

"What I saw in the Oval Office yesterday was a willingness to engage with each other in a sincere way - air disagreements, listen," McHenry said after one of the meetings last week.

Biden aides say the relationship between Biden and McCarthy is largely cordial and businesslike and that Biden recognizes the Speaker has a struggle on his hand presiding over the various factions within the Republican Party.

TRUMP, PELOSI CONNECTIONS

It may not help their relationship that both men were very close to the other's predecessor.

Biden idolized former Democratic House Speaker Nancy Pelosi, a woman "who I think will be considered the greatest Speaker in the history of this country," he said at his Feb. 7 State of the Union address.

McCarthy was an enthusiastic supporter of Biden's predecessor, Republican Donald Trump, and a frequent flyer on Air Force One when Trump was president.

He was among 147 Republicans who voted to overturn Biden's 2020 election win over Trump's claims of election fraud, although he eventually acknowledged Biden as the legitimate president.

He criticized Trump over his failure to rein in his own supporters during the Jan. 6, 2021, attack on the U.S. Capitol, but remains in touch with him.