"They can contemplate all they want to, but the reality is if they want a figurehead chairman you can have a figurehead chairman, but it won't be Michael Steele," he said.
Steele aides insist the chairman was not threatening to quit, but merely to fight over retaining his authority. But his comments reflect the persistent tension within the Republican National Committee over his chairmanship.
On Wednesday, RNC state chairmen will vote on the funding issue, among others -- such as whether to label the Democratic Party "Socialist."
For now, members are expected to re-establish standards that had already been in place before they lapsed last year. Among them is a requirement that Steele have a co-signer for all expenditures above $100,000 and that a comptroller-treasurer administer funding.
Steele had already agreed to those standards. What he objected to was the possibility of increasing the powers of the comptroller-treasurer, in turn minimizing his own authority. That issue will probably be pushed off until July, but it's not going away yet.
Steele, who delivered a speech Tuesday on the future of the GOP, said some of the animosity is from people in the party who supported other candidates for chairman. But some of his critics are former allies.
"Some of them were supposedly friends that were in some cases, when I was a young state party chairman, were mentors to me and it's kind of eerie to see them standing on their knives bared," he said.
Some friction comes from Steele's misteps and gaffes. Some comes from his firing of numerous RNC staffers when he took office. A small-but-vocal minority of long-time RNC members is leading the charge against Steele.
Committee members say all they want is financial accountability in the RNC management.
FOX News' Carl Cameron and Jake Gibson contributed to this report.