Pro-labor forces appear en route to win an important battle in Ohio on Tuesday, but the greater war they’re engaged in is very much undecided. As significant as issues like taxes, bargaining, and benefits are for the health of the country’s public sector unions, their real savior has largely gone unspoken in this most recent battle—namely, the bolstering of pay and benefits in the private sector. Progressives will no doubt be tempted to celebrate their victory—not least because it marks a setback for Governor Kasich, and a good omen for Obama’s struggle for this key swing state in 2012—but they should also be wary of myopia.

Anti-labor forces certainly have their eyes set on the broader terrain. When Wisconsin’s Governor Scott Walker recently declared that “public employees can’t be haves, while private sector employees are have-nots,” he was peddling an obvious half-truth, but also suggesting the outlines of a pernicious anti-labor strategy. Republicans gladly acknowledge the divide in our economy that often places many of private sector workers on the side of have-nots—only to exploit it by mobilizing resentment against those with relative security. Public unions should be thinking of ways to help pull up their embattled fellow laborers in the private sector—or risk being dragged down themselves.

THE LATEST POLLING in Ohio gives the pro-labor forces a 25 point lead in the referendum to repeal legislation that effectively gutted collective bargaining for the state’s public workers. The unions appear to be succeeding for a number of reasons. First, there does seem to be an important groundswell—from Wall Street to Oakland—against these dramatic attacks on working people. Beyond that, the most important factor is labor’s pouring of massive funds into the struggle, which puts this on a financial par with a stiff gubernatorial race. Also at play is Republican hubris, evidenced by their inclusion of firefighters and police in the legislation. Safety workers are both beloved and conservative—at least until their turf is attacked. Then they tend to shun their social conservatism and turn out the troops.

But the promise of Tuesday’s vote as a pro-labor harbinger is undermined by the persistent weakness of private sector unions in Ohio and elsewhere in the country. Indeed, the successes of public sector employees have always been closely linked with that of laborers in the private sector: it’s largely private sector workers, after all, who are asked to pay for public sector employees through their tax receipts. Having the mega-rich pony up will certainly help—especially in a place like New York City—but outside the worlds of finance capital, working people are going to be paying a good share bills.

Unfortunately, the numbers here tell a dispiriting story. Today 36.2 percent of public workers are organized—a slightly higher number than the private sector was even in the heyday of American labor history in the 1950s. Private workers today, in contrast, have tumbled to a mere 6.9 percent—a figure suggestive of the wider rot in pay and benefits among unorganized workers. It doesn’t take a labor scholar to see the problem here: A relatively large and well-remunerated public sector is teetering precariously on a rickety and crumbling private-sector working class.