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The RNC conservatives’ move could put pressure on Mr. Steele.

His allies on the RNC have privately argued against the 80 percent rule, which sponsors want to have debated and put to a vote at the January meeting of the RNC in Honolulu.

The last time a resolution to bar funding to Republican candidates was attempted was in 1991, when social conservative Tim Lambert, an RNC member from Texas, narrowly lost a floor vote on his proposal not to help pro-choice Republican candidates.

Some of the party’s most prominent figures, including former Chairman Haley Barbour, now Mississippi governor, were flown into the meeting to speak against the Lambert resolution, arguing that it was a litmus test and thus did not comport with the GOP’s “big tent” philosophy.