In an era of declining union membership, Nevada has remained a stronghold of sorts. Last year, 16.4 percent of workers there were represented by unions, according to the Bureau of Labor Statistics, which is an increase from the 14.3 percent of workers represented by unions a decade ago. In Wisconsin, the opposite is happening. Just 12.5 percent of workers were represented by unions last year, compared to 16.9 percent a decade ago.

Percentage of Workers Represented by a Union

Data: Bureau of Labor Statistics/Datawrapper

Nevada has seen an increase in union membership in part because of the success of the Culinary Workers Union, which organized housekeepers and kitchen workers and now represents 55,000 workers. As a result, many of the people working in the state's many hotels and casinos make well above minimum wage, and the Culinary Union wields considerable power on and off the strip.

The Culinary Union and other Las Vegas labor groups have grown even though Nevada is a right-to-work state, where state law prohibits members from being compelled, as a condition of their employment, to pay union dues. Still, in Nevada, most members agree to pay them—in 2012, 90 percent of the members of Culinary 226 opted to pay dues.

That's because reform-minded leaders in the culinary union were able to convince rank-and-file members that being in a union benefits their families, said Harley Shaiken, a professor at Berkeley who studies labor. For example, the unions say they have helped workers access a middle-class lifestyle by bargaining on their behalf for higher wages. Nonunionized workers in similar jobs in other parts of the country make minimum wage; Las Vegas workers made $16 an hour, or more. Without dues-paying members, much of that would not have been possible: In Wisconsin, dues-paying members dropped off significantly as a part of labor reforms, leading unions to lay off staff and cut back on advocacy.

“The net result is that they transformed that union in Las Vegas, and Las Vegas became a model nationally for what might be done,” he said. “It showed that organizing is possible and that effective organizing raises the possibility of a middle-class lifestyle.”

Through organizing the state's growing Latino population, unions also became a powerful political contingent in Nevada. Unions were instrumental in helping reelect incumbent Senator Harry Reid in a closely-fought race in 2010, both by contributing money and by setting up efforts such as a worksite initiative where construction and casino workers lobbied others to vote for Reid, and a door-to-door campaign effort staffed by union members. Reid has recently announced his intentions to run again for the seat in 2016.

Many observers think it's the unions' political muscle that is the true target of GOP leaders in Nevada. If unions were the key piece to reelecting Harry Reid in 2010, a decimated labor movement could make his reelection attempt in 2016 more daunting than it already is. Nationally, Democrats will need to hang on to seats such as Nevada if they want to regain control of the Senate in 2016—and Republicans hold the other Nevada Senate seat. A weakened labor movement in Nevada could also spell trouble for Democrats in a presidential race: The state is still a swing state, and has a good track record for picking presidents.