U.S. Republican presidential candidates Rick Santorum and Mitt Romney are in a tight race in Michigan, while Romney is enjoying a lead in Arizona, ahead of primary elections in those states next week.

An average of polls in Michigan shows Santorum and Romney in an extremely competitive race , as contenders Newt Gingrich and Ron Paul trail far behind. In Arizona, the average shows Romney with an eight-point lead over Santorum's 30 percent support.

However, an average of national polls for the Republican nomination shows Santorum has a clear lead, with nearly 34 percent support, over Romney's 28 percent.

The Republican candidates took part in a nationally televised debate Wednesday night in Arizona, for their first such meet-up since January.

Santorum and Romney argued about each other's record on government spending.

Romney said Santorum had voted five times to increase the maximum debt the U.S. could have, a point he has repeated on the campaign trail. Santorum countered that Romney had said he supported a debt ceiling increase last summer and wanted to raise taxes on the top one percent of U.S. earners, which Romney denied.

Texas Representative Ron Paul accused Santorum of being a “fake” conservative who professed one stance while campaigning, did something different while in office, then pledged to repeal programs he had supported.

Political analysts say the debate could leave a strong impression on voters in Arizona and Michigan.

Then, on March 6, voters in 10 states head to the polls in what is known as “Super Tuesday,” as they choose a challenger to take on President Barack Obama, a Democrat, in November's general election.