US unions confident of passing organizing measure

* Unions say organizing law to be introduced soon

* Opponents say move ill timed given recession

* Democratic senators in Wal-Mart's home state said to be wavering

By Andrew Stern

CHICAGO, March 4 (Reuters) - Big U.S. labor unions expressed confidence on Wednesday that they have enough votes in Congress to pass long-blocked legislation to boost their organizing efforts, while opponents said they do not.

"We're confident we haven't lost any support from the successful effort two years ago -- or near-successful," said Bill Samuel, the AFL-CIO's legislative director in a conference call from the labor coalition's winter meetings in Miami.

The legislation, the Employee Free Choice Act (EFCA), was first introduced in 2003 and easily passed the Democrat-led U.S. House of Representatives in 2007 but was eight votes shy of the 60 votes in the Senate needed to end debate and prevent a procedural block by Republicans.

Then-President George W. Bush had also promised to veto the legislation.

But President Barack Obama, a former community organizer and a Democrat who won powerful support from organized labor in last year's election, has long indicated he favors the bill.