A plurality of South Dakota's likely voters say Sen. John ThuneJohn Randolph ThuneTrump plan to claw back billion in spending in peril McConnell: Mueller 'ought to wrap it up' Graham jokes about Corker: GOP would have to be organized to be a cult MORE (R) should make a run for the White House in 2012.

Forty-one percent of Thune's constituents said their senator, who's expected to cruise Nov. 2 to reelection for a second term, should run for president, according to a new Argus Leader/KELO-TV survey released on Monday.

But 35 percent of the state's likely voters said Thune, the fourth-ranking GOP senator, should not challenge President Obama in 2012, while 24 percent of South Dakotans were undecided.

The survey, conducted by Mason-Dixon Polling & Research, suggests Thune might have a window of opportunity to pursue a run for president without having to worry about alienating home-state voters who might be frustrated if he were to decide to run. Serious campaigns for the White House require extensive out-of-state focus, often in states that hold nominating contests early in the 2012 cycle.

Republican voters were especially supportive of a Thune candidacy, with 55 percent saying they'd support a presidential campaign. A plurality of independent voters in the state, 41-29 percent, said they would support Thune if he were to run.

Thune's been coy about his ultimate intentions, though he's been among the handful of Republicans to steadily crack open the door toward deciding to run. He told the Argus Leader that the new survey was all "hypothetical."

The poll, conducted Oct. 20-21, has a 3.5 percent margin of error.