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With an ongoing move afoot among some members to oust Mr. Steele in the hope of repairing the RNC’s damaged image in time to raise sufficient funds — $60 million or so — needed to help House and Senate candidates in the November elections, the Steele team has fought back, with Mr. Steele accusing critics of racism and his allies circulated a letter asking members to pledge support.

At last count, 58 of the RNC’s 168 member had signed the letter, thus appearing to ensure that any motion to oust him would fall short of the supermajority required. For members and party elders who think his remaining as chairman will do more damage than ousting him, a voluntary and graceful exit on his own appears to be the only option — unless more gaffes take place under his stewardship that are so egregious that some of those 58 signers say enough is enough.

Mr. Pullen was one of the 110 members who refused to sign the letter of support for Mr. Steele.

“I support the RNC as an institution, but I don’t know why anybody has to sign a letter” like that, Mr. Pullen told The Times.

Calls for Mr. Steele’s resignation had grown by Thursday when North Carolina GOP Chairman Tom Fetzer, who has been a staunch Steele supporter, wrote him saying, “I have prayed for you and hurt with you these last few weeks. I thank you for the passion you have brought to the job of leading our party, which is one of the reasons I have been a strong supporter of you during my tenure as chairman of the North Carolina Republican Party.”

“The point is to deal with the reality of a situation that is becoming increasingly untenable,” Mr. Fetzer wrote. “Without going into a lot of detail about the situation we find ourselves in, I offer my personal opinion that the best way for you to deal with the reality of the situation is to tender your resignation. I neither arrived at this conclusion lightly nor derive any pleasure from articulating it to you.”

Mr. Steele and the RNC’s spending and fundraising problems are paramount topics among Republicans who began gathering in New Orleans for the privately financed Southern Republican Leadership Conference, which is not an RNC or state-party event.

E-mails from members have been circulating among attendees calling for Mr. Steele to step down for the good of the party whose candidates for Congress normally rely on RNC donations to augment funds provided by the GOP House and Senate campaign committees. But the RNC has spent more than it has raised since Mr. Steele became chairman in January 2009.

“We would like to see Chairman Steele succeed, but there is a lot of [RNC] members coming here to New Orleans telling me about their concern over the way things are going at the national committee,” Mr. Villere said.

Mr. Steele’s statement last week that Republicans who criticize him and President Obama are motivated at least in part by racial considerations appears to be hurting the RNC with potential grass-roots allies on the right.

“I do not like the reports of Steele trying to use the ‘race card’ as a defense mechanism,” Waco, Texas, “tea party” organizer Toby Marie Walker said Thursday. “By stating that he falls into a different ‘margin of error’ because he is black is utterly ridiculous, he shouldn’t use his race as a defense any more than I should use being a woman if I were in his shoes.”

Mrs. Walker, echoing the concerns of many conservatives, added that the recent outrage wasn’t about race but “donor money being used for purposes that do not reflect the family values the RNC [supports].”

Mr. Barbour said in a CNN interview on Sunday that Mr. Steele was wrong to say that race motivated his critics, saying “in that job, people are judged by results.”

But Mr. Barbour, who was national chairman in the early 1990s, declined to criticize Mr. Steele, saying “I do think it’s not right for a former chairman to critique his successors. I just don’t think that’s something that I ought to do. I kind of feel the same way President Reagan was about future presidents.”

Earlier versions of this article incorrectly named well-known conservatives who turned down invitations from Republican National Committee Chairman Michael S. Steele last weekend. Rep. Ron Paul, NRA Executive Vice President Wayne LaPierre and Family Research Council President Tony Perkins should not have been listed among the numerous officials who had turned down invitations to speak at some fundraising events in New Orleans.