DETROIT (Reuters) - Mitt Romney edged ahead of rival Rick Santorum in Michigan's Republican presidential primary on Tuesday as the former front-runner fought to avoid a humiliating defeat in the Rust Belt State where he grew up.

With 61 percent of precincts reporting, Romney led Santorum by 40 percent to 36 percent. Texas Congressman Ron Paul claimed 12 percent and former House Speaker Newt Gingrich had 7 percent.

In Arizona, Romney rolled to an easy victory. Television networks declared him the winner there as soon as polls closed at 9 p.m. EST (0100 Wednesday GMT).

But the stakes are particularly high for Romney in Michigan, where he was born and raised and where his father was a popular governor in the 1960s. Romney won the state in his failed 2008 White House bid.

A defeat would raise more questions about his ability to appeal to conservatives and blue-collar voters in the state-by-state battle to take on Democratic President Barack Obama in the November 6 general election.

Aides said Romney has the funds and organization to win his party's nomination even if he loses Michigan.

Republican Party leaders, concerned that Santorum's religious conservatism could make him unelectable against Obama, may feel pressured to search for a new candidate to join the race.

No matter what the outcome, Romney will likely end the evening with a greater lead over his rivals in securing the 1,144 delegates needed to win the nomination. Arizona awards its 29 delegates on a winner-take-all basis, while Michigan awards its delegates on a proportional basis.

An ABC News/Washington Post poll found Romney at a new low among the most conservative Americans. He is viewed favorably by just 38 percent of that group, the poll showed, down 14 points from a week earlier, while 60 percent view Santorum positively.

'A LITTLE BIT LIBERAL'

I've always liked Santorum but it's more what I don't like about Romney. He is just saying he is a conservative and I do not believe him, said August Vortriede, 53, of Farmington Hills.

Santorum's campaign urged Democrats to vote in the open primary, but exit polls showed that Democratic participation was not significantly greater than in previous Republican contests.

(Additional reporting by Eric Johnson in Michigan and Lily Kuo, Patricia Zengerle and Patrick Temple-West in Washington; Writing by Andy Sullivan; Editing by Doina Chiacu)