That means that the coalition supporting overhaul starts from a position of strength, although Representative Tom DeLay of Texas, the House majority whip, has vowed to do all he can to defeat the bill.
As head of the cabinet department that oversees the I.R.S., he said part of his motivation for supporting overhaul efforts "is not liking to be at the top of an organization that gets the level of ridicule and criticism for its inability to administer the tax code the way it is".
As Republicans have been searching with fresh intensity in recent weeks for a new approach to the divisive issue of immigration, the poll provides potentially heartening information to lawmakers who have urged the party to support overhaul legislation that would eventually allow illegal immigrants to become citizens.
Still, Mr. Alexander's estimates have been widely cited by those who support overhauling Medicaid.
The insurance lobby would not support overhauling the system without the individual mandate.
He opposes the death penalty and strongly supports overhauling New York's Rockefeller-era drug laws, for example.
"We need the money," said Len Nichols, a health economist at the New America Foundation, which supports overhauling the current insurance system to give more people access.
On Capitol Hill, though, many lawmakers remain opposed to the ban, including Senator Kirsten E. Gillibrand of New York, who has long supported overhauling the earmark process and who was among the first lawmakers to place her own requests online.
A dozen members of the clergy who support overhauling the health care system recently met with the congressman's rabbi, who said he would talk to Mr. Adler about the legislation.
Still, Senator Dianne Feinstein, the California Democrat who is chairwoman of the Senate Intelligence Committee, said she supported overhauling the program but keeping it in place because it generates information that might prevent attacks.
The Senate Finance Committee is to hold hearings on 527 groups on July 12. "We have the momentum, we have the policy, we have the votes," said Fred Wertheimer, president of Democracy 21, a group that supports overhauling campaign finance law.
