Did McCain want to switch parties in 2001?

According to this report in The Hill, several Democrats claim that Sen. John McCain discussed with them the idea of switching parties in 2001, shortly before Sen. Jeffords abandoned the Republicans. The Jeffords switch gave the Dems a majority.
Former Democratic Senate leader Tom Daschle makes this claim, as does former Rep. Tom Downey, who at the time was a lobbyist. Supposedly, two months of negotiations ensued after a top McCain aide, John Weaver, made an approach to his friend Downey on the Senator’s behalf. Ted Kennedy, Harry Reid, and John Edwards all participated in the alleged courtship. Senator McCain denies the report, insisting “I never considered leaving the Republican Party, period.