CHICAGO (AP) – Illinois Republicans insist they can still win the U.S. Senate race with the right candidate to replace Jack Ryan who abandoned his bid for Congress after scandalous sex club allegations became public.

But political analysts say it will take a full-blown miracle.

Republicans began mulling over possible candidates soon after Ryan stepped down Friday, just four months before the election. He is accused of trying to pressure his former wife, television actress Jeri Lynn Ryan, to have sex in public. Ryan has denied the allegations.

Kent Redfield, a political science professor at the University of Illinois in Springfield, said Sunday that a Republican winning the seat of retiring GOP Sen. Peter Fitzgerald was “an almost impossible task.”

With many well-known Republicans striking themselves off the list of potential candidates, Republicans have a dearth of choices who have the statewide name-recognition needed to challenge Democratic state Sen. Barack Obama, who held a wide lead even before the scandal broke.

The Republican candidate also faces a shortage of time and money.

Kick-starting the campaign of lesser-known Republicans would cost several million dollars, Redfield said, adding that many donors are likely to flinch at the prospect of contributing to what many regard as a doomed campaign.

“If it looks unwinable, it is very difficult to raise money,” he said. “You can’t win because you can’t raise money, and you can’t raise money because you can’t win.”

To have even a slim chance of victory, the candidate should meet certain qualifications, said Charles Wheeler, head of the Public Affairs Reporting program at the University of Illinois.

“To start out with, it has to be a candidate who has no skeletons in the closet, who is articulate and who can raise money,” he said. “It would help if they found someone who is a gazillionaire.”

Republicans have said they would begin interviewing possible candidates in the coming days, with the aim of naming one by mid-July.

Redfield said the best Republicans can hope for is to prevent a bad situation from becoming worse – and to ensure that the U.S. Senate candidate at least doesn’t hurt other Republicans in tight races for state offices.

“They wanted to put a new face on the Republican Party and that was supposed to be Jack Ryan,” said Redfield. “Now, they just want to look credible and stop the bleeding.”

Former Gov. Jim Edgar, one of the prominent Republicans who said he is not willing to pick up the baton from Ryan, rejected the notion that time is running out to run an effective campaign.

“Some states haven’t even had primary elections yet,” Edgar told the (Carbondale) Southern Illinoisan at a rally Saturday in Benton. “The fact we have four months to go gives more than enough time for a candidate to make his or her case. I remain optimistic that we can hold on to that seat.”