A tough fight for Michigan between Mitt Romney and Rick Santorum tightened on Monday in a primary that may prove pivotal in choosing a 2012 Republican presidential nominee.

With Michigan to vote on Tuesday, a new poll said Santorum had halted a slide in support that began after a weak debate performance in Arizona last week.

The Mitchell Research/Rosetta Stone poll said the former Pennsylvania senator is in a statistical dead heat with Romney, edging him 37 percent to 35 percent after losing the lead last week. The poll's margin of error was 3 percentage points.

The volatility we thought had changed has not. The race remains very fluid, said Steve Mitchell, president of Mitchell Research & Communications, a Republican firm that polled 858 Republican primary voters.

Romney has a comfortable lead in Arizona, which also votes on Tuesday.

A Romney victory in Michigan - the state where he was born - would reignite a campaign staggered by Santorum's rise. But a loss would be humiliating and raise significant questions about his candidacy a week before the biggest one-day prize of the primary season, March 6 Super Tuesday when 10 states hold contests.

Romney told voters in Albion, Michigan that he was gaining momentum. This sure has been fun these last 10 days or so. We started out about 15 points down in the polls. Now we're leading in the polls, he said.

A Santorum win in Michigan could upend the race and prompt the Republican establishment - concerned that Santorum's strong religious conservatism could make him unelectable - to search for a new candidate to join the race, which picks a challenger for the November 6 election against Democratic President Barack Obama.

After days of attention on his opposition to contraception and prenatal testing, Santorum sought to focus on the U.S. economy, the main issue in the 2012 presidential campaign.

CAMPAIGN ABOUT THE ECONOMY

In a Wall Street Journal opinion article, Santorum called for just two income tax rates and approval of the controversial Keystone oil pipeline from Canada. He vowed to make $5 trillion in budget cuts over five years.

I'll work with Congress and the American people to once again create an economic environment where hard work is rewarded, equal opportunity exists for all, and families providing for their children can once again be optimistic about their future, he wrote.

In making his economic pitch, Santorum blasted Romney's record as a former governor of Massachusetts and said his rival's plan to cut tax rates for all Americans by 20 percent did not go far enough.

He also vowed to repeal all Obama administration regulations that have an economic burden over $100 million, including an Environmental Protection Agency rule on carbon emissions.

In the Michigan town of Rockford, Romney returned fire, and suggested that Santorum had spent too much time on social issues, saying: I'm glad he recognizes this has got to be a campaign about the economy.

Romney, whose vast wealth has been an issue in the Michigan campaign, promoted himself as the candidate with the most business experience needed to trigger job growth.

Senator Santorum is a nice guy, but he's never had a job in the private sector. He's worked as a lobbyist, worked as an elected official, and that's fine. But if the issue of the day is the economy, I think to create jobs it helps to have a guy as president who's had a job, and I have, Romney said.

The two candidates trekked across Michigan to make closing arguments and try to encourage voter turnout.

In Livonia, Santorum said he was excited at his position.

This was not a place that frankly I thought we were going to be competing at the level we're competing here in the state of Michigan, he said.

In a sign he has emerged as a leading contender, Santorum will be getting Secret Service protection beginning on Tuesday, a campaign aide told CBS News.

(Additional reporting by Sam Youngman in Livonia and Susan Heavey and Patricia Zengerle in Washington; Editing by Alistair Bell and Cynthia Osterman)