(Reuters) - Arizona Gov. Jan Brewer, who had a finger-pointing confrontation with President Barack Obama last month, on Sunday endorsed Mitt Romney for president.

He has that pro-business background and he has that political history that I think ... would serve America the best, Brewer said of Romney, who squares off with rival Rick Santorum in Republican presidential primaries on Tuesday in Arizona and Michigan.

Appearing on NBC's Meet the Press, the Republican Brewer announced her endorsement of Romney, saying: I think he is the man who can carry the day.

Romney, a former private equity executive and Massachusetts governor, leads in polls in Arizona. Polls show a tight race with Santorum in Michigan.

Brewer last month engaged in a tense exchange with Obama as she greeted his plane, Air Force One, in her state. During a brief encounter on the tarmac, intended to be a ceremonial welcome, Obama told Brewer he disagreed with an account she had given of a meeting they had at the White House two years ago.

He was a little disturbed about my book, 'Scorpions for Breakfast,' Brewer told reporters afterward. At one point during their chat, she pointed a finger at the president.

Brewer has differed with Obama over immigration policy. In 2010 she signed a state law requiring police in Arizona to check the immigration status of anyone they detain and suspect of being in the nation illegally. Other provisions require immigrants to carry their papers at all times and ban people without proper documents from soliciting for work in public places. The U.S. Supreme Court will decide the fate of the law.

Sen. Lindsey Graham, R-S.C., again declined to endorse any of his party's candidates.

But Graham, during an appearance on CNN's State of the Union program, said Romney has improved as a candidate and would avert a major setback in Michigan.

If Romney had lost Michigan, and he is not going to lose Michigan, that would have thrown things into the ditch, Graham said. I think he is going to win both states.

Romney really has sharpened his skills and I think that will pay dividends if he gets the nomination, Graham added.

Sen. John McCain, R-Ariz., who has endorsed Romney, also said on CNN that he expects the Republican presidential primaries to eventually produce a candidate around whom the party can rally.

I am confident Mitt will do well on Tuesday night in Arizona and in Michigan and hopefully that will move this process and so we can concentrate on the real adversary, McCain said, referring to Obama.

(Reporting by Thomas Ferraro, Jackie Frank and Caren Bohan; Editing by Will Dunham)