Senate Majority Leader Harry Reid (D-Nev.) said Democrats would pay for President Barack Obama’s $447 billion jobs bill with a new tax on millionaires.

“The American people believe it is time for millionaires and billionaires to pay their fair share to help this country thrive,” Reid said on the Senate floor Wednesday.

The move will help unite Democrats who had been fractured over the assorted tax increases proposed by the president, and it draws a sharper contrast with the GOP, assuming that they vote en masse to block the package.

The millionaire tax idea has been proposed before — a version was voted on by the Senate last year — and, as Reid noted, has strong support in public polls. But Republicans have argued against raising taxes, particularly given the weak economy.

Reid and Senate Minority Leader Mitch McConnell (R-Ky.) also continued to spar over how to bring up the jobs package. McConnell wants a vote on the package as is — so it can be killed — while Reid is demanding a debate and the opportunity to amend it.

McConnell took aim at the president.

“Stop campaigning for a bill written in a way to guarantee it won’t pass and work with us on the kind of job-creating legislation both parties can agree on,” he said.