“We never stopped talking to Sen. Specter. This certainly gives us more opportunity to talk to him and address our concerns about his position on the Employee Free Choice Act,” said Bret Caldwell, a spokesman for the Teamsters.

Labor leaders have been hunting for the 60 votes needed to overcome a threatened Republican filibuster on the bill. They’d found themselves about a vote short and had leaned heavily on Specter to close the gap.

Thus far, he has refused and, in a statement announcing his party switch, he said his opposition to the legislation would not change.

But Specter has always left some wiggle room in his position by opposing its current language and offering suggestions about how it might be improved.

In fact, Teamsters President James P. Hoffa attended a meeting with Specter on Monday to discuss the legislation.

Specter’s party switch will make his relations with labor leaders all the more important since Pennsylvania is a state with a large union membership that votes Democratic.

The Teamsters have 80,000 members in the state and the AFL-CIO and the Service Employees International Union are also heavily represented.