The daily tracking poll, the first done since Wednesday's presidential debate, put the former Massachusetts governor and Michigan native at 40 percent, The New York Times reported. Santorum, a former U.S. senator from Pennsylvania, got 34 percent.
Rasmussen found that in a national match-up with President Obama, both Santorum and Romney would lose if the vote was held now. Santorum would get 42 percent of the vote and Romney 41 percent to 48 percent for the president.
Arizona and Michigan hold their primaries Tuesday. Michigan is considered critical for Romney because of his close ties to the state, where his father was a popular governor.
Rasmussen conducts its daily tracking surveys with 500 interviews per night, averaged over a three-day period. The margin of error for the entire sample is 3 percentage points.