By Thomas Ferraro and Kevin Drawbaugh

WASHINGTON, Jan 27 (Reuters) - The Democratic-led U.S. Congress on Tuesday gave final approval to what may be the first bill signed into law by President Barack Obama -- a measure to reverse a 2007 U.S. Supreme Court decision that made it tougher to sue for wage discrimination.

On a vote of 250-177, the House of Representatives passed the measure, which sailed through the Senate last week, 61-36.

The bill now goes to Obama, who took office one week ago after actively supporting the legislation last year while campaigning for the White House with the strong support of labor unions and women, who are paid 23 percent less than male workers in the United States.

A top priority of organized labor, the bill would lift tight time restraints to file claims that could expire before workers realize they were treated unfairly.

The measure would "correct a disastrous Supreme Court ruling that allows bad employers to discriminate against their employees as long as they hide it for 180 days," said Illinois Democratic Representative Phil Hare in a debate on the House floor.

Republicans have agreed with many in the business community that the measure could trigger an explosion of lawsuits based on old claims, discourage employers from hiring women and undermine efforts to stem the recession.

"The bill invites more and costlier lawsuits," said California Republican Representative Howard McKeon.

The Lilly Ledbetter Fair Pay Act is named for an Alabama woman who lost her wage discrimination lawsuit in the Supreme Court in 2007. After 19 years on the job, Ledbetter sued her employer when she discovered that she was the lowest-paid supervisor at the Goodyear Tire & Rubber Co plant, despite having more experience than several male co-workers.