WASHINGTON – The Senate voted Tuesday to ease campaign funding restrictions on candidates battling wealthy, self-financing rivals, overriding objections that the move would run afoul of the Constitution and undermine an effort to reduce the role of money in politics.

At the same time, Sen. John McCain predicted that limits would be raised for all candidates by the time debate on campaign finance legislation was through. “The only question is how much,” he said.

For a second straight day, McCain, R-Ariz., and his allies labored to hold together a bipartisan coalition behind their attempt to reduce the campaign money chase. At day’s end, they succeeded in killing a politically appealing proposal to curb donations by lobbyists, saying it was unconstitutional as drafted and could doom their entire effort.

Supporters of the amendment relating to millionaires said it was necessary to equalize an advantage that flows to any candidate able to use a personal fortune to finance a campaign. Four Democrats did so last year – Sens. Jon Corzine of New Jersey, Mark Dayton of Minnesota and Maria Cantwell of Washington, all first-termers; and Sen. Herb Kohl, D-Wis., who was re-elected. Kohl and Corzine supported the amendment; Dayton and Cantwell opposed it. Maine’s senators, Olympia Snowe and Susan Collins, voted for the amendment.