Mitt Romney has a narrow lead over Rick Santorum in Arizona, according to a new CNN/TIME poll.

The former Massachusetts governor takes 36 percent of likely Republican voters in the state, with former Pennsylvania senator Santorum close behind at 32 percent. Former House speaker Newt Gingrich is in third place with 18 percent, while Texas Rep. Ron Paul is a distant fourth at 6 percent.

Thirty-four percent of respondents said they were open to changing their minds.

Arizona’s Feb. 28th contest, along with the primary in Michigan the same day, will be the first serious test of Santorum’s momentum and Romney’s perceived weakness.

CNN is hosting a debate in Arizona on Wednesday night.

Romney’s Arizona campaign has undergone a bit of turbulence in the past few days. His state campaign co-chair, Pinal County sheriff Paul Babeu, resigned over the weekend in the wake of allegations that he threatened to have a former lover deported.

While Santorum has vaulted to the top of polls in the wake of his victories in Colorado, Minnesota and Missouri earlier this month, no delegates were assigned in those states and Romney was not focused on them.

Arizona is a winner-take-all state with 29 delegates.

Romney generally outperforms his rivals in the West. So although Michigan is the make-or-break state for him next week, a loss in Arizona would not look good either.

Santorum is currently leading in Michigan polls.