Four of the five Republicans on the committee were ready to move ahead, said Rep. Doc Hastings, the panel's Republican chairman. The panel also has five Democratic members.
The Republicans were "prepared to vote at the earliest opportunity to empanel an investigations subcommittee to review various allegations concerning travel and other actions" by DeLay, he said.
CBS News Correspondent Bob Fuss reports the unusual offer was an effort to break a deadlock that has basically shut down the ethics committee. After the bipartisan panel admonished DeLay three times last year, the committee's Republicans were replaced and the rules changed to allow either party to bar any investigation.
But Democrats gave no ground. They said they wouldn't allow the evenly divided committee to conduct investigations unless Republicans reversed a rule providing for automatic dismissal of cases.
Senior committee Democrat Alan Mollohan of West Virginia quickly rejected the offer, saying his party would continue blocking the panel unless a bipartisan task force was appointed to write new rules for investigating lawmakers.
"The first principle in doing it right is that it be bipartisan," said Mollohan. "That's a beginning point for me."
Mollohan would not say whether he supported an investigation of DeLay, commenting that his effort to change the rules is ``totally independent from any specific case.''
DeLay has said repeatedly he hopes to appear soon before the panel to clear up questions about his actions.
The Texan has come under intense scrutiny in recent months, in part over questions about overseas trips he took over the past several years.
DeLay and other Republicans have insisted in public comments in recent weeks that the charges against him were partisan in nature, the efforts of a minority desperate to regain power.
At the same time, there has been growing restiveness among members of the GOP rank and file who were unhappy to be on the receiving end of questions about whether they were merely trying to shelter DeLay from harm.
Hastings would not comment on whether he had spoken to DeLay about the proposal but he did say he could not speak with a member "about matters that may or may not come before the ethics committee."
Meanwhile, more questions are being raised about DeLay's ethics. An Associated Press review found that DeLay treated his political donors to a bird's-eye view of a Three Tenors concert from an arena skybox leased by a lobbyist now under criminal investigation.
DeLay's political action committee did not reimburse lobbyist Jack Abramoff for the May 2000 use of the skybox, instead treating it as a type of donation that didn't have to be disclosed to election regulators at the time.