The Federal Assembly, made up of both houses of parliament in Berlin as well as an equal number of representatives from the states – a total of 1244 delegates – is set to hold the first ballot around noon.
The centre-right coalition of Angela Merkel's Christian Democrats (CDU) and the pro-business Free Democrats (FDP) have a total of 644 delegates, which is 21 more than the absolute majority needed to elect their candidate Wulff, who is currently the premier of Lower Saxony.
However there has been some wavering in their ranks, with at least four members of the FDP vowing openly that they would vote for Gauck, a Protestant pastor and former dissident in communist East Germany, and several more refusing to reveal how they will vote.
The big question is whether there are enough other dissenters in the closet to tip the vote Gauck's way or at least force a second and third ballot, giving Gauck added momentum.
The vote is widely seen as a crucial test for Chancellor Merkel, who is already weakened by her lukewarm performance and the constant bickering within her coalition since last September's election. Though the job as head of state is largely ceremonial, the controversies and fierce debate this time around have lended a heavy political significance to the position.
The process was triggered by the surprise resignation exactly 30 days ago of President Horst Köhler over controversial remarks he made about the Afghanistan war, which he said was partly being fought for economic reasons.
Wulff, meanwhile, expressed confidence Tuesday evening that he could win in the first round.
“There is a fair chance that it will come together in the first ballot, but no one knows,” he said.
Further complicating matters is the possible support for Gauck of the socialist Left Party and the Free Voters, a bloc of non-party affiliated members of various parliaments, who have also expressed a preference for Gauck but will vote independently.
The Left is fielding its own candidate, Luc Jochimsen, a former TV journalist and now a Left MP. If she is knocked out in the first round, the question becomes whether the party will support Gauck. General Secretary Dietmar Bartsch pleaded with his party Tuesday night to keep an open mind if it came to a second ballot, though some MPs, Jochimsen herself included, have said they would not vote for Gauck under any circumstances.
An absolute majority – or more than 50 percent of the votes is needed to win the first or second ballots. If no candidate gets an absolute majority in either of these, then the third ballot is decided on a relative majority, meaning the candidate with the most votes wins.