WASHINGTON - Since losing 30 seats and their 12-year stranglehold on power in 2006, House Republicans have kept asking themselves the same question: Can it get worse?

On Tuesday, they may get another answer they won't like.

With lots of help from Washington -- including more than $1.3 million in campaign cash and a last-minute visit by Vice President Dick Cheney -- Mississippi Republicans are desperately trying to retain a congressional seat in one of the most reliably conservative districts in the nation.

The stakes in the 1st District special election couldn't be higher, strategically or symbolically. The loss of a traditionally GOP seat to a Democrat would be the third in a special election this spring and the second in the Deep South after the May 3 victory of Rep. Don Cazayoux, D-La.

Rank-and-file Republicans say that would force a day of reckoning for their leadership.

"When you connect three dots in anything, that's a bad thing. This connects the dots. At that point, everybody's got to come together and have a come-to-Jesus meeting," said Rep. Tom Davis, R-Va., a retiring centrist who will help form a new advisory panel at the National Republican Congressional Committee.

Democratic leaders have stopped tamping down expectations and instead have set a new goal for the November elections of establishing a long-lasting majority that could dominate the chamber.

"We will have a strong, confident, predictable Democratic majority to take us forward, and then we will be in 2010, 2012, on the path to a strong Democratic leadership for a long time to come," said House Speaker Nancy Pelosi, D-Calif.

And, just when Republicans thought they had seen everything, Rep. Vito Fossella, R-N.Y., admitted Thursday that he has a 3-year-old daughter from a long-running extramarital affair with a retired Air Force officer. Fossella, who is married and has three young children at home in Staten Island, is also facing drunken-driving charges in Virginia. GOP strategists are debating whether he should resign or announce that he will not seek re-election in November.

Fossella's resignation would mean another special election, this one in the nation's most expensive media market.

No more excuses

Independent analysts agree that a loss Tuesday would leave Republicans with no excuses. They blamed poor candidates in races in Louisiana and Illinois, where the GOP lost a special election for the seat long held by former House speaker J. Dennis Hastert.

"The Republicans would be ignoring reality if they try to explain away this race," said Nathan Gonzales, political editor of the Rothenberg Political Report.

Since 1994, Republican Roger Wicker has been re-elected to his House seat with between 63 percent and 79 percent of the vote.

But with Wicker appointed to the Senate to fill the seat vacated by Trent Lott, who retired, Republicans are having difficulty unifying behind Greg Davis, the mayor of Southaven, a Memphis suburb in the northwest corner of the 1st District. Davis beat a Republican from the eastern portion of the district in the March primary. That win puts Davis on the ballot in November, whether he wins or loses this week's special election.

Democrat Travis Childers, a court officer in Prentiss County, came within a few hundred votes of outright victory in the first round of special-election balloting April 22, prompting national Republicans to send out an SOS for Tuesday's runoff.

Davis, the NRCC and conservative allies have flooded the airwaves with a multimillion-dollar campaign that tries to negatively tie Childers to Pelosi and Sen. Barack Obama, D-Ill.

This is the second special election this month in which House Republicans have tried to turn the race into a referendum on a Democratic candidate's ties to Obama. The strategy was unsuccessful in Louisiana, but Republicans view the Mississippi district as more receptive because it is slightly more conservative and has fewer black voters.

The NRCC already has committed $1.3 million to the approach in Mississippi, triple the amount it spent in Louisiana.

Mississippi Gov. Haley Barbour, a former Republican National Committee chairman, has collected donations for Davis from party committees in such far-away states as Pennsylvania and Michigan. Cheney arrives this evening for a get-out-the-vote rally.

"Republicans are committed to winning in Mississippi, and we believe the momentum is on our side," said Ken Spain, NRCC spokesman.