Call it musical chairs, Republican-style.

A behind-the-scenes scramble is under way inside the Missouri GOP as potential candidates handicap their chances to take on Democratic U.S. Sen. Claire McCaskill next year.

Former Republican senator Jim Talent’s announcement last week that he will not seek his old seat has opened the door to a crowded field of maybes in a contest that the national party has made a priority in 2012.

“It’s an indication of Sen. McCaskill’s vulnerability that you do see a number of potential opponents taking a close look at this race, particularly so early on in the cycle,” said Brian Walsh, spokesman for the National Republican Senatorial Committee.

The only hopeful so far to officially announce that she’s in is former state treasurer Sarah Steelman. But the race could pick up some more star power if some of the maybes eventually launch campaigns. Now considering the race are:

•U.S. Rep. Sam Graves, a six-term House member from northwest Missouri, whose district includes parts of Kansas City.

•U.S. Rep. Jo Ann Emerson, a nine-term member from the Bootheel.

•Ann Wagner, an experienced political operative who headed the Missouri GOP, held a top post at the Republican National Committee and was ambassador to Luxembourg. She just lost an attempt to chair the Republican National Committee.

•Ed Martin, a former chief of staff to Gov. Matt Blunt, who ran a competitive race for Congress last year but lost to Democratic incumbent Russ Carnahan of St. Louis.

All of them are gauging their ability to raise millions of dollars to unseat a senator. Graves issued a poll by SurveyUSA on Thursday showing that he has the best shot of any Republican against McCaskill.

The survey showed McCaskill winning a hypothetical race, but only 48 to 44 percent, a split right at the poll’s 4 percent margin of error.

If Talent had run, it’s likely that Emerson, Wagner and Graves would not have entered the race. But with Talent out, a period of intense maneuvering has commenced with candidates, or their representatives, holding quiet meetings to gauge intensity of interest.

Graves, who just raised his political profile by becoming chair of the House Small Business Committee, might defer to Wagner if she runs, aides said. He is also friends with Steelman, which “obviously weighs into it,” Graves said.

Meanwhile, Wagner called Graves “a marvelous congressman” and said, “I will be speaking with him.”

Steelman angered members of her party when she ran against Kenny Hulshof for the 2008 GOP gubernatorial nomination. Hulshof won, but he wound up losing decisively to Democrat Jay Nixon — a loss that many blamed on the primary.

But Steelman reinforced her GOP bona fides by backing Republican Roy Blunt for the Senate last year.

McCaskill declined to comment on the potential Republican field, except to say that Missouri is a “very difficult state.”

Whatever combination of contenders for her seat emerges could foreshadow a lively and hard-hitting primary, something Republicans generally try to avoid.

Hulshof said a primary can be good or bad. Bad because primaries often divide parties. Good because they allow candidates to battle-test their campaigns.

He placed his contentious 2008 primary against Steelman on the bad side.

“It was such a difficult primary that there were supporters of my primary opponent that we were never able to bring into the fold,” he said.

Wagner said she hopes that the potential candidates “can all sit down” and work it out.

For Democrats, GOP infighting would be a dream come true, especially since McCaskill’s poll numbers aren’t scaring anybody. The Graves survey showed that 48 percent of Missouri voters approved of the job she is doing, while 45 percent disapproved.

“A divisive Republican primary would be disastrous for Republicans and godsends for Democrats,” said Missouri State University political scientist George Connor. “This definitely is good news for Claire McCaskill.”

Democrats were pasted in last fall’s elections. Next year, they need to defend more Senate incumbents than the Republicans.

While the economy is showing signs of improvement and President Barack Obama’s approval rating is edging upward, he’s still unpopular in the state.

McCaskill is one of his closest allies in Congress. Republicans are expected to attack her for supporting health care reform and other administration initiatives.

But Democrats cautioned that McCaskill shouldn’t be underestimated, and Graves agreed.

“She’s just a tough campaigner,” he said. “Her votes are very out of step with Missouri. Having said that, just because you’ve got all the votes on your side doesn’t mean it will be easy.”