RALEIGH, N.C.—By all rights, Asheville city councilman Carl Mumpower should be a rare political specimen this year, a Republican with a plausible shot at ousting a Democrat from Congress, Rep. Heath Shuler.

Turns out he is something far more common: a GOP challenger burdened with an assortment of political and personal problems in addition to President Bush’s unpopularity and economic hard times.

It’s a familiar story across the country. Republicans are having a tough time mounting respectable challenges against Democratic incumbents, even green first-termers in conservative-leaning districts.

In addition to a campaign cash disadvantage that vexes challengers of all stripes, this year’s cast of GOP challengers is paddling against a forbidding current of bad economic news that voters tend to blame on whichever party is sitting in the White House.

Still, there always are one or two exceptions to the rule. This year they’re in the Houston-area district represented by Democratic Rep. Nick Lampson, who won a seat that for two decades had been the domain of former Republican leader Tom DeLay, and in Pennsylvania’s Wilkes-Barre-Scranton area, setting of “The Office” TV comedy series.

DeLay’s resignation under a cloud of scandal cleared the way for Lampson’s return to Congress in 2006. Lampson formerly had represented another district in Texas until DeLay’s redistricting plan for the state after the 2000 census basically gerrymandered him out of office.

But Lampson’s new district is overwhelmingly Republican and he has a formidable challenger in Pete Olson, a Navy veteran and a protege of popular Republican Sen. John Cornyn and former Sen. Phil Gramm. The Lampson-Olson race is considered one of the most competitive in the country.

In blue-collar, heavily Democratic northeastern Pennsylvania, Hazelton Mayor Lou Barletta has become somewhat of a Republican star in his challenge for 12-term incumbent Paul Kanjorski’s House seat.

Kanjorski finds himself in the toughest re-election fight of any veteran House Democrat after catching flak for steering nearly $10 million in federal contracts to a now-bankrupt technology firm controlled by relatives. “He did good, but he did good for himself too,” said Joe Kutz, 75, a retired factory worker and one-time Kanjorski supporter. “It’s time for him to move on, get out.”

Barletta has been a charismatic staple of talk radio and cable TV news shows after winning measures—later struck down as unconstitutional—to punish landlords who rent to illegal immigrants and businesses that employ them. He enjoyed a 9-percentage-point lead in a poll last month by Franklin & Marshall College.

Not in the tossup category are almost all other Republican efforts to unseat majority Democrats.

Mumpower’s challenge in North Carolina to Shuler, for example, has lost any muscle to which it once aspired.

Shuler is a Democratic high school football hero who went on to play for the NFL’s Washington Redskins. In 2006, he ousted eight-term incumbent Rep. Charles Taylor, who was weakened by attacks on his business dealings and his own distaste for campaigning.

The GOP hoped to retake the district in the state’s western mountains before Shuler had a chance to solidify his base. It seemed a promising opportunity for Republicans to knock off a Democrat, until a rapid-fire series of developments in Mumpower’s world soured it.

Mumpower declared that Bush should be impeached, stunning many supporters and party loyalists. Three local GOP committees severed ties with his campaign. Then Mumpower’s son, who was working as his campaign manager, was arrested in Asheville after a bar fight. Now the GOP challenger is having trouble raising money.

“It would be the upset of the year, right now, if he were to defeat Shuler,” said Bill Sabor, a political scientist at the University of North Carolina at Asheville.