Of likely voters 47 percent said they thought the Republican candidate was likely to beat President Obama, while 39 percent said they expected Obama to win re-election. Fourteen percent said they were undecided.
Voters also gave the edge to the GOP to win control of the U.S. Senate and retain its majority in the House of Representatives, Rasmussen Reports said.
The Iowa caucuses kick off the primary cycle Tuesday.
Results are based on a nationwide telephone survey of 1,000 likely voters conducted Tuesday and Wednesday. The margin of error is 3 percentage points.