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Mr. Terpeluk resigned in mid-December without a formal announcement or explanation.

Mr. Steele did not respond to a question e-mailed and telephoned to his press aide as to whether he would replace Mr. Terpeluk before the Jan. 14 election or wait until afterward, to fill the post if Mr. Steele wins re-election.

If Mr. Steele is replaced, the appointment of a finance chairman is likely to be a top priority for the RNC boss.

Gentry Collins, who quit last year as Mr. Steele’s chief of staff and publicly blasted his leadership, said the RNC’s base of major donors has withered with Mr. Steele at the helm.

“The choice of finance chairman is crucial any time, but especially with this unprecedented debt, and obviously I’ve given a lot of thought to who would be ideal for the role,” Mr. Collins, who ended his quest to replace his former boss at the RNC’s helm Sunday, told The Times.

Mr. Collins, 35, has considerable experience in top staff positions for Republican committees and candidates, but accumulated the fewest public commitments from RNC members.

“Ann [Wagner], Maria, Reince [Priebus], and Saul [Anuzis] are all outstanding candidates, and any of them would move the committee in a positive direction,” Mr. Collins said in his resignation statement.

Michigan RNC member Anuzis is savvy with new media, is considered reliably conservative and is popular with many members. However, he lags league leader Priebus when it comes to first-round committed votes for the chairmanship. Mr. Anuzis, 51, said he has had his mind on things other than finance chairman.

“I’m currently planning on co-chairs with a team of regional co-chairs as well,” he told The Times. “It’s going to have to be a ‘team approach’ to make this work.

“Besides, it’s too early to be talking to specific fundraisers,” Mr. Anuzis said, “That would be putting the cart before the horse.”

Mr. Priebus, 38, is a successful Wisconsin Republican chairman and was RNC general counsel and Steele chief adviser until he, too, resigned abruptly last month. Mr. Priebus won’t divulge whom he is considering for the finance post but told The Times that “naming a finance chairman and a top-notch chief of staff would be the very first of priorities.”

Asked how long it would take him to name both, he said, “Those activities would be immediate.”

Ranking at this point just ahead of the last-place Mr. Collins, the normally taciturn Ms. Cino told The Times that she would name more than one finance chairman — and do it fast.

“It is extremely important to name national finance co-chairs as quickly as possible, which is what I have proposed,” she said, adding that she has in mind “a few folks that have demonstrated great abilities in the past.”

It is Mr. Priebus, however, who is unique among the candidates because he has behind-the-scenes backing of powerful establishment Republicans such as Mississippi Gov. Haley Barbour and the unexpected public endorsement of constitutional lawyer Jim Bopp.

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