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Mr. Steele, who described himself at one point as a “half-glass-full kind of guy” countered that the RNC under his leadership did not have “72-hour get-out-the-vote program, we had a 12-month get-out-the-vote program.”

“The idea that we didn’t fully fund [get-out-the-vote programs] is a misnomer because this year we had to play in all 50 states,” he said.

He said the RNC provided local GOP officials with technology and other aid, citing the GOP takeover of the House and more than 20 statehouses in November as proof of the effectiveness of his approach.

Asked by debate co-moderator Tucker Carlson of the DailyCaller website what would disqualify a Republican candidate from receiving RNC help, the candidates agreed that it would be failure to back 80 percent of the GOP platform.

But Mr. Steele cautioned against using “litmus tests” to judge fellow Republicans — the same objection he raised in initially opposing a resolution by conservatives on the committee earlier in his term that applied the so-called “Reagan 80 percent test” of loyalty to party candidates.

The rivals for chairman have been crisscrossing the country — at their own expense or with help from backers — seeking support from the 56 party chairmen and the two other national committee members in each of the 50 states and five territories.

Former Deputy Transportation Secretary Maria Cino drew applause when she answered co-moderator Grover Norquist’s question to name the biggest mistake Republicans made in the past 10 years.

Her response was “McCain-Feingold,” referring to the campaign-finance regulation law enacted by a Republican-led Congress and signed by President George W. Bush. Mr. Priebus, who raised record donations as Wisconsin party chairman in the 2010 elections in which Republicans candidates swept the board in his state, also warmed conservative hearts when he said the next RNC leader will have to “play well in the sandbox with the tea party movement. … We’re not in competition with the conservative movement. We’re part of it.”

Americans for Tax Reform, the DailyCaller and the Susan B. Anthony List hosted the debate at the National Press Club.