As Rep. Stephanie Herseth Sandlin ponders a bid for South Dakota governor, Democratic leaders in Congress are quietly urging her to run for re-election.

“They are making it clear they want me to stay,” Herseth Sandlin said. “The conversations have started in the last couple of weeks. I’m trying to decide by the August recess.”

Herseth Sandlin isn’t the only incumbent whose ambitions are causing some heartburn in the higher ranks of Congress.

Leaders of both parties are trying to figure out what to say or do to hang onto about 10 ambitious lawmakers who are undecided about possible races for other elective offices.

So far, 12 House members have already committed to bids for statewide offices: six for governor, five for U.S. senator and one, Adam H. Putnam of Florida, for state agriculture commissioner.

Based on a review of House records, the most House members to run for governor or senator over the past two decades was 16 in 1994.

Senior members of both parties say the cadre of members pondering campaigns for other offices has been fed by frustration with the growing competition for plum committee assignments and elected leadership jobs, by restrictions on the perquisites of seniority (like GOP term limits for ranking members) and by the grueling demands of biennial re-election campaigns. In addition, some longtime political observers say House members have been inspired by the example of President Obama, who made the transition from state legislator, to senator to chief executive in just over four years.

Artur Davis , D-Ala., a candidate for governor, says Democrats are being pulled away from Congress by the perception that statehouses are less plagued by gridlock, and by frustration with long waits on the seniority ladder. “You have to build a career here to become a chairman,” Davis said.

Minority Whip Eric Cantor , R-Va., said Republican leaders are urging incumbents to help win back a House majority. And with Senate Democrats close to a filibuster-proof majority, Cantor added: “The prospects of taking over the House, I believe, are better than that which you would see in the Senate.”

In addition to Herseth Sandlin, others facing tough choices in coming weeks include potential Senate candidates such as Michael N. Castle , R-Del.; Joe Sestak , D-Pa., and Peter T. King , R-N.Y.; and possible gubernatorial contenders Peter A. DeFazio , D-Ore., and Greg Walden , R-Ore.; and Jim Gerlach , R-Pa.

The product of a family with deep ties in South Dakota politics, Herseth Sandlin, who was elected in 2004 at age 33, is much in demand. She was the first woman from South Dakota to win a general election to Congress and is a member of the fiscally conservative Blue Dogs.

Herseth Sandlin says she’s been getting gentle pitches to seek re-election from Chris Van Hollen of Maryland, chairman of the Democratic Congressional Campaign Committee, and other members of Speaker Nancy Pelosi ’s, D-Calif., leadership team.

”I’m letting them know the factors that I’m considering. And I’m letting them know the pressure I’m getting on the other side,” said Herseth Sandlin, referring to requests from party activists to enter the governor’s race.