By Brendan O'Brien

MADISON, Wis. (Reuters) - Wisconsin unions bused in thousands of workers from around the state on Saturday to demonstrate against the impending adoption of a law that would ban private sector workers from being required to join a union or pay dues.

The bill, which was approved by the Republican-led state Senate on Wednesday, would make Wisconsin the 25th state to adopt a so-called "right-to-work" law. It is supported by Governor Scott Walker, a potential Republican presidential candidate.

About 5,000 people gathered at the state capitol on Saturday, despite the frigid temperature of 16 degrees F (-9 C). The protesters waved U.S. flags, rang cow bells and chanted "This is what Democracy looks like." Many held signs denouncing the bill.

William Carroll, a Teamsters business representative from West Bend, called on workers to become more active in their unions.

"If we don't do this, we will die a death of a thousand cuts," he told the crowd.

Walker became a favorite of some in the Republican Party in 2011 when he pushed for a law to limit the power of public sector unions shortly after becoming governor. His support grew when he survived a union-backed recall election in 2012.

The Wisconsin AFL-CIO organized Saturday's rally, which comes four years to the month after massive demonstrations at the state capitol by workers opposed to the limits then under consideration covering most unionized public sector workers.

Union members chanted "shame" as senators voted narrowly to approve a right to work law on Wednesday and moved it to the state Assembly, also controlled by Republicans, where a public hearing is scheduled for Monday.

Opponents cast the bill as an assault on organized labor and blue-collar workers that would limit union revenue and further erode the political power of organized labor. Supporters contend it could help to attract more jobs to Wisconsin.

Mark Buss, 59, a hardhat-wearing union member from Appleton who was at Saturday's rally, said that in order to survive, unions must educate younger workers about the value of organized labor.

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"The bigger issue is equality for all workers," he said.

The full Assembly is expected to vote on the measure within a week and Walker's spokeswoman has indicated he will sign a bill if it gets to his desk. The measure as written would take effect upon the governor's signature.

(Reporting by Brendan O'Brien; Editing by Mary Wisniewski, Bill Trott and Bernard Orr)