WASHINGTON » The race in North Dakota for a Senate seat being vacated by a retiring Democrat, Kent Conrad, was supposed to be a cakewalk for Republicans. When the state’s lone House member, Rick Berg, entered the contest, leading Republicans tucked the seat into their pocket and looked to other battles in their quest for a Senate majority next year.

It has not worked out that way. The U.S. Chamber of Commerce has announced it would spend $200,000 broadcasting advertisements promoting the energy positions of Berg, the Senate candidate and House freshman. The nonpartisan Cook Political Report downgraded the race to a toss-up.

And Berg’s Democratic challenger, Heidi Heitkamp, a former state attorney general, has begun tearing into his brief record in the terribly unpopular House of Representatives.

"The people of North Dakota, like the people of this country, believe Washington, D.C., is badly broken," Heitkamp said.

Republicans, who need a net gain of only four seats to guarantee control of the Senate, have long been optimistic that they could capture the majority because they are defending just 10 of the 33 seats up for grabs. But their task is complicated by many of their candidates being sitting or recent members of the House, which polls show to be deeply unpopular.

In the 15 races ranked as most competitive by The , Republicans could field current or recently departed House members in eight of them; Democratic House members are top candidates in four Senate races.

Races that were not supposed to be all that close are looking more like barn-burners, in large part because one of the standard-bearers carries the millstone of his or her current position: member of the House.

House membership is "more a liability than I’ve ever seen it," said Stuart Rothenberg, editor of the nonpartisan Rothenberg Political Report. "We go through periods when Congress is less popular than other times, but congressional approval ratings right now are so abysmally bad, so unbelievably bad, it has to rub off on members seeking higher office."

Just west of North Dakota, Montana’s endangered freshman Democratic senator, Jon Tester, is going up against the state’s lone House member, Denny Rehberg. Todd Akin, a veteran Republican representative from Missouri, is in a tough primary to decide whether he will challenge Sen. Claire McCaskill, who is considered vulnerable.

Rep. Jeff Flake, R-Ariz., remains favored to take the Senate seat of Sen. Jon Kyl, who is retiring. But Flake faces a spirited challenge from a former U.S. surgeon general, Richard H. Carmona, running as a Democrat and an outsider against what he calls "a chronic politician." And Rep. Connie Mack, R-Fla., has an uphill fight to unseat Sen. Bill Nelson, a Democrat.

Democrats have their own struggles. The Senate contest in New Mexico between Rep. Martin Heinrich, a Democrat, and former Rep. Heather Wilson, a Republican, is considered close. In Wisconsin, Republican campaign operatives are hammering the House record of Rep. Tammy Baldwin, a Democrat, as she gears up her campaign for a Senate seat. The House records of both Rep. Shelley Berkeley, D-Nev., and Dean Heller, appointed to the Senate from the House, will feature heavily in their Senate contest.

And in the toss-up race for an open Senate seat in Hawaii, former Gov. Linda Lingle, a Republican, is likely to brand her once-favored challenger, Rep. Mazie Hirono, a creature of the hated House.

But comparatively speaking, the problem in some races may be especially acute for Republicans, who must contend with the both Congress’ overall approval rating and the damage that has been done to the Republican brand, Rothenberg said.

Members are making the best of it.

Rehberg said individual members of Congress were "not as unpopular" as the institution itself. Besides, "Montanans don’t sit around saying, ‘Boy, I hate Congress.’ That’s something for the pollsters and the media to feed — and do," he said.

Flake said his record of angering leaders of both parties with his crusade against pet projects financed by so-called earmarks — a crusade that led to his removal from the House Appropriations Committee — would inoculate him from attack.

"I could see how it would be seen as a negative for some if they’re seen as just part of the institution, but if you’re seen as fighting the institution, it’s a plus," he said.

But Democrats happily emailed around links to a Web video put together by Flake’s Republican challenger for the Arizona Senate nomination that portrays Flake as a career politician, and Carmona campaign aides say Flake’s reputation as a rebel is more a fixture of Washington than Arizona.

Opponents eager to tie all the House members seeking a Senate seat to the body they are leaving will make few distinctions. The National Republican Senatorial Committee last week tried to tar Rep. Joe Donnelly, D-Ind., a Roman Catholic alumnus of the University of Notre Dame, with the Obama administration’s requirement that health insurance plans provided by Catholic charities and universities offer free birth control to women. Donnelly is running for the seat of Sen. Richard G. Lugar, a Republican.

Baldwin, of New Mexico, was criticized for missing House committee votes on an energy bill but making time to appear on Ed Schultz’s liberal radio show. After Baldwin introduced legislation codifying President Barack Obama’s "Buffett Rule," which would increase the tax rate for many people who earn more than $1 million a year, Republicans denounced her for seeking to raise taxes on "American families and small businesses."

Mack, of Florida, was hit both for House votes he took, like opposing an increase in the debt ceiling, and votes he missed, like repealing the president’s health care law.

The North Dakota race has been among the major surprises as it has tightened due, at least in part, to dissatisfaction with the perceived performance of Berg, who did not respond to repeated requests for comment.

To exploit any weakness, Heitkamp is going hyper-local with her campaign. While Berg talks up conservative national issues like a balanced budget amendment to the Constitution, she emphasizes budget cuts to the U.S. Highway 83 Bypass at Minot, road repairs at Devils Lake and air service subsidies to Jamestown.

Rehberg acknowledged that his House seat puts him in a tight spot. The message that Tea Party voters sent in 2010 was that Republicans should stand firm on deep spending cuts, regardless of the consequences. But independent voters are now howling at what they see as Republican obstructionism and demanding more cooperation.

"It creates conflicting things in the governing mind," Rehberg said. "That’s why this is going to be a very close election."

© 2012 The New York Times Company