Republican Mark Sanford needs a breakthrough moment in tonight's debate for South Carolina's congressional special election, or else his comeback effort to win on 7 May is likely to fall short against Democrat Elizabeth Colbert Busch.

Sanford hopes to return to public office as a congressman, after resigning his in the wake of an extramarital affair for which he resigned from the governor's mansion and left his wife. After winning the Republican nomination for the special election in South Carolina's first district, Sanford has faced a barrage of bad press suggesting that he can do no good, even including the news that he violated the terms of his divorce with his former wife.

His Democratic opponent, businesswoman Elizabeth Colbert Busch, has her own claim to fame. Her brother, Stephen Colbert, has hosted numerous fundraisers on behalf of his sibling, helping her stay on the air in a district that went for Mitt Romney by over 15pt. She has also received support from a number of outside organizations, like the Democratic Congressional Campaign Committee.

The National Republican Congressional Committee, meanwhile, has abandoned Sanford. They refuse to air advertisements on his behalf, leaving the airways to his opponents. Sanford himself has little money left, and has been forced to rely on tactics such as a "debate" last week – with a cardboard cutout of Nancy Pelosi. He couldn't afford podiums. Sanford used music stands instead. As a smart analyst told me, "It just feels like he's going down."

The one poll we have from the race shows Sanford trailing by 9pt, 50% to 41%. The poll, conducted last week by Public Policy Polling (PPP), shows an electorate that has Democrats as a greater proportion of the vote compared to PPP's prior survey, which Colbert Busch led by 2pt. The new poll's respondents voted for Romney over Obama by only a 5pt margin, compared to the 18pt margin Romney by which won the district last fall. PPP attributes this difference to low Republican enthusiasm, itself stemming from the most recent charges against Sanford.

Not everyone is buying PPP's survey, though. Cook Political Report's Dave Wasserman, for instance, thinks that Colbert Busch leads, but by a margin less than 9pt. My own math indicates that when you adjust PPP's projected electorate to match its prior survey, Colbert Busch is ahead by a little over 3pt.

So just what are the chances that PPP's poll is off by 9pt? Not very likely.

Over the past ten years, there have been 30 non-candidate/party sponsored polls conducted in the final two weeks before 18 off-cycle (i.e. not on election day during a midterm or presidential year) special congressional elections. Overall, these polls have been mostly accurate; 27 out of 30 times, the candidate leading in the poll won most of the votes in the special election. (Note: I only look at those elections where at least one Democrat and Republican are running. You can see the raw data here.)

Two of the three polls after in which the leading candidate didn't win the election were for the 2009 New York 23rd special election, a unique race, in that there were three competitive candidates: Democrat Bill Owens, Republican Dede Scozzafava and Conservative Party candidate Doug Hoffman. In the week prior to the election, the Republican candidate dropped out, remained on the ballot, and endorsed the Democrat.

Not surprisingly, the 23rd special had PPP's largest absolute error; they predicted Conservative Hoffman to win by 17pt. He lost by 2pt to the Democrat.

In 26 of the 30 special election surveys, the polling error was less than 9pt – Colbert Busch's lead. The polls' average error was only 4pt, and the median even lower, at 3pt.

These margins leave little room for Sanford. He would need an error of at least 9pt, which has happened only 13% of the time. He would also need that error to be in his favor, which means he's looking at a 7% likelihood. That's not outside the realm of possibility, but it's a long shot. My guess is internal polling shows the same results, which is why the Cook Political Report and Rothenberg Political Report have put their finger on the scale for Colbert Busch.

The best comparison to this scenario would be Louisiana's sixth special election in 2008. Louisiana's sixth was like South Carolina's first in that a Republican represented the district for over 30 years, and both districts were over 15pt more Republican on the presidential level than the nation as a whole in the prior presidential election. Like Sanford, Republican Woody Jenkins had run for statewide multiple times. Jenkins also had his own ethics problems: a connection with former KKK wizard and Louisiana politician David Duke.

The final poll before the Louisiana sixth special had Democrat Don Cazayoux ahead by 9pt, just like the recent poll that shows Democrat Colbert Busch leading. Jenkins did better than his numbers suggested. He didn't lose by 9pt, but he did lose – by 3pt. Even though the poll overestimated Jenkins' deficit, Cazayoux's lead was too great to overcome.

Like in Louisiana's sixth, there is a decent chance that the upstart Democrat's lead is less than 9pt. It's quite possible Republican voters will come around to Sanford on election day.

The chance, however, that the PPP poll is so off that Mark Sanford defeats Elizabeth Colbert Busch? Less than 15%, unless something happens very quickly.