I found an article that goes into why they are so scared. It is because labor, with 250,000 volunteers, did the hard pick and shovel work of turning out the vote all around the country. This includes in targeted congressional seats. This is a big change from focusing on the base. Having these grassroots activists in competitive districts can help ensure that the candidates that campaign on labor's issues follow through at the policy level.
This is how the San Francisco Chronicle sums it up:
Under the proposed law, if a majority of employees at a workplace approve by signing authorization cards, a union will represent the group.
An Obama win meant everything to labor, because Sen. John McCain is an ardent opponent of the legislation, and labor's ground game was impressive: Unions spent about $450 million in the election, and the effort was particularly helpful in battleground states. In all, union members connected with 13 million voters in 24 states, in the process selling the Employee Free Choice Act along with the Democratic ticket.
However, the Democrats did not get a filibuster proof majority. Democrats currently have 58 Senators. In order to get the bill through the Senate, the bill's proponents must be able to stop a filibuster and that requires 60 votes.Here is a link to the AFL-CIOs Free Employment Act Page.