Jefferson's seat is one of the nation's last unresolved midterm races, and he would become the only Democratic incumbent to lose if his re-election bid fails.
The eight-term congressman was forced into the runoff against a fellow Democrat after he failed to win 50 percent of the vote in a crowded open multiparty primary. His opponent, state Rep. Karen Carter, is seeking to become the first black woman from Louisiana elected to Congress.
After being abandoned by the state and national Democratic parties and unable to attract large sums of cash, Jefferson has turned to old allies to forge a grass-roots campaign that has kept the race tight despite his legal problems.
Jefferson, 59, has been handicapped by a wide-ranging investigation into allegations that he took bribes — including $90,000 allegedly found in his freezer during an FBI raid — from a company seeking lucrative contracts in the Nigerian telecommunications market. He has not been charged with any crime and denies any wrongdoing.
The scandal has turned the race into a debate largely divided along racial lines, an age-old dynamic in this city that has intensified since Hurricane Katrina displaced large numbers of blacks and upended their demographic and political dominance.
Whites, who overwhelmingly voted for Carter in the primary and have been her most enthusiastic financial backers, believe a Jefferson win would confirm this city's image as corrupt and untrustworthy as it asks the nation to fund its recovery from Katrina.
Jefferson has drawn widespread support among blacks who are skeptical of the federal government's motives in its investigation of him. He has repeatedly suggested the probe is groundless because he has yet to be indicted more than a year after the FBI raided his home in New Orleans.
Despite the race's ostensible importance, residents here don't seem motivated to vote. Turnout in the primary was an estimated 22 percent — low for a city that loves its spicy politics. Saturday could see even fewer voters because the congressional race is the only item on the ballot. The primary ballot was plump with constitutional amendments.
"People are distracted, they're rebuilding," pollster Silas Lee said. "And it's Christmas."
Carter, 37, has raised nearly five times as much money as Jefferson, but she's been largely outflanked in the endorsement game. Jefferson has picked up the backing of Mayor Ray Nagin and other prominent black politicians.
The endorsements speak to Jefferson's solid footing in New Orleans politics. He arrived here in the 1970s as a Harvard-educated lawyer from the backwaters of north Louisiana, the sixth of 10 children brought up in a three-room country home. By 1980, he represented New Orleans in the state Senate. At 42, he became the first black from Louisiana in the House since Reconstruction.
And the law firm Jefferson founded became the largest black-owned practice in the South. He created a political organization, the Progressive Democrats, which fielded candidates for the school board, assessors' races, state House seats and mayoral contests.
Before the bribery scandal erupted, Jefferson had climbed to the pinnacle of the Democratic Party. He was a confidant of former President Bill Clinton and held a seat on the powerful House Ways and Means Committee.