The slate that wins the most seats in the new parliament will have first shot at choosing a prime minister, although the designee will need the support of two-thirds of parliament. The Shiite bloc is expected to get the most votes, but if Allawi's slate wins enough seats, he could step in with a coalition that covers the political spectrum.
"To them, he's the No. 1 opponent," said political analyst Hassan Bazaz, referring to the Shiite slate.
"They know what the other groups will get," he said. "They know Allawi will be able to form alliances. They know he's on very good terms with the Kurds, and they know he will go ahead and form an alliance with the Sunnis."
Still, Allawi, who needs to do much better at the polls than he did in January, may have trouble shedding the perceptions about his past.
Among many Shiites, he is tarnished by his membership in Hussein's Baath Party during the 1970s, before he went into exile. Among Sunnis, said White, "he's still Shiite. To top it all off, he's an exile who received CIA funding."
Speculation has been widespread that Allawi is among the candidates favored by the British government and, to a lesser extent, Washington, largely because of his secular views. He denies foreigners are involved in his well-financed campaign.
On a recent afternoon, during a break between visitors, Allawi appeared relaxed despite the Najaf attack a day earlier. Just one subject raised his temper: being targeted for his Baathist past.
"I fought more than anybody else to unseat this regime of Saddam and I suffered tremendously, my family suffered a lot," he said. "What, they'll come back to me again and say, 'Thirty, 40 years ago you were a member of the Baath Party'? ... This is becoming a joke."
With few reliable polls, it is difficult to predict who will hold sway Thursday. Allawi believes many voters will make up their minds in the last few days.
His posters seem to be everywhere, and they bill him simply as "Allawi." The implication: Fame is to be known by one name only. A horse, taut and poised for a jump, has been incorporated as a logo. Glossy leaflets depict Allawi as a statesman, visiting military leaders and scientists and posing in front of mosques and churches.
At his campaign operations center, a dozen people sat around a large table, monitoring the Internet. "When someone attacks, we reply instantly," said Saad Yousif, a media strategist. "It's like firefighting."