Mitt Romney swept into Ohio Tuesday to talk about how much he agrees with Republican Governor John Kasich’s aggressive approach to budget issues. He even visited a call center where Republicans were trying to stir up support for Kasich’s signature initiative: a sweeping assault on labor rights so controversial that it faces a “citizen veto” in a November 8 statewide vote.

But, with new polling showing that Ohioans are overwhelmingly opposed to Kasich’s law (a fresh Quinnipiac University poll has voters favoring the repeal of the anti-labor law by a 57–32 margin), Romney blurred the message. Instead of the expected encourargement of a “yes” vote to keep the law on the votes, Romney praised Kasicg and then waffled on the referendum—saying he’s leave the issue up to the voters. It was a messy moment in a messy campaign.

So what the heck was Romney doing in Ohio? Why was the Republican presidential contender veering off his own campaign trail to spend time in a state that won’t hold its presidential primary until June of 2012? And why was he struggling to play all sides of the labor fight?

What’s happening in Ohio this fall is about more than Ohio.

The vote on Kasich’s anti-labor law—which was scheduled after 1.3 million Ohioans signed petitions supporting a repeal effort—is a key contest in the “Karl Rove” primary. Rove has not endorsed a candidate for the Republican presidential nomination. But he’s pretty obviously leaning toward Romney—just ask the recently affronted Herman Cain. Romney wants to be where Rove says to go; he also wants Kasich’s endorsement, as part of a strategy that seeks to reprise the game plan Rove constructed for George W. Bush in 2000, which counted on the backing of Republican governors to help secure the GOP nod.

Rove has for months been indicating that Republicans had better put Ohio on their schedules this fall if they want support next fall.

Since March, when Governor Kasich and his legislative allies moved to strip away the collective-bargaining rights of Ohio’s state, county and municipal employees, as well as teachers—and to render their unions politically dysfunctional—Rove has led the cheering section.

The former White House political czar, who promises he that groups he controls will spend $250 million nationally in the upcoming election cycle, has:

§ set up a Government Union Reform Action Center to coordinate anti-labor work in states such as Ohio and Wisconsin

§ written columns for the Wall Street Journal about the Ohio and Wisconsin fights

§ appeared frequently on Fox News to talk up the importance of what Kasich—an old political ally—has done

§ launched a cable advertising campaign attacking the unions that have fought Kasich and the Democrats who have aligned with them

§ made Ohio a regular stop on his speaking and political consulting schedule, visiting as recently as late September.

Why the fascination?

Rove has always been obsessed with breaking up and breaking down public-employee unions. On the list of the issues that his heavily funded group Crossroads GPS ranks as top priorities, the highest-ranking specific fight is against organized labor in the states. “It’s time,” declares the message from Rove’s Government Union Reform Action Center, “government stood up for American taxpayers, not the unionized bureaucrat elite.”

Ohio’s November 8 referendum vote has become mission-critical for the people who pull the strings in the national Republican Party, and the network of conservative groups that has powered the party’s surge since the US Supreme Court’s Citizens United ruling allowed for unlimited corporate donations to supposedly “independent” organizations.

Rove has made no secret of his determination to protect Kasich and the anti-labor law that was enacted in March despite mass demonstrations by unions and their allies. The Ohio law is actually more draconian in its efforts to diminish the role of unions in the workplace and in political campaigns than the measure that was enacted at the behest of Wisconsin Governor Scott Walker, and that excited Rove. “Both sets of reforms give local and state governments flexibility to deal with budget shortfalls and looming deficits, rein in unfunded pension liabilities, return control of personnel policies to elected officials, and end counterproductive workplace practices demanded by unions,” chirped Rove in March. “Yet all in all, labor law experts consider Ohio’s new law stronger, broader and more wide-ranging than Wisconsin’s.”

Rove didn’t just talk up the Ohio labor law change. He put his money where his mouth was.

In March, Rove’s Crossroads GPS group launched a $750,000 cable television advertising campaign that demanded to know, “Why are Democrats shutting down state capitols to protect a system that pays unionized government workers 42% more than non-union workers?”

That was a false claim; an Economic Policy Institute study found that public employees were actually under-compensated in comparison with their private-sector counterparts.

The advertising Rove aired in March attacked not just public-employee unions but President Obama, claiming that he was aiding unions that—through their political activities—pose “a threat to democracy.”

It was an absurd charge.

But Rove wasn’t worried about truth or falsehood.

The political strategist was putting his marker down, identifying the Ohio fight as central to the Republican and conservative causes.

He hasn’t backed off. According to the Columbus Dispatch, the shadowy group that was set up to preserve Kasich’s anti-labor law—Building a Better Ohio—expects to spend as much as $20 million on this fall’s campaign. And it is Building a Better Ohio that has been  a Rove-style campaign to confuse Ohio voters, and to demonize public employees and their unions.

Building a Better Ohio is running a big-budget campaig. And so are other groups, such as Make Ohio Great—which is backed by Republican operatives and donors around the country—and Liz Cheney’s Alliance for America’s Future, which are playing big in a campaign that will see the same level of spending as a hotly contested gubernatorial or US Senate contest. In fact, the tens of millions spent in Ohio will rival what was spent to win the state in recent presidential elections.

How much of that money is coming from Rove and the billionaire CEOs and hedge-fund mangers associated with his American Crossroads and Crossroads GPS groups? Building a Better Ohio isn’t saying. The group was established as a nonprofit 501(c)4 organization, so that it doesn’t have to reveal its donor list.

The same goes for Make Ohio Great, Cheney’s Alliance for America’s Future and other groups that are backing Kasich’s position.

But no one imagines that Rove—whose Crossroads groups were big players in Ohio in 2010, who promises that they will be even bigger players in 2012 and who has been so outspoken in his support for Kasich’s anti-labor initiative—has been sitting on the sidelines.

Thousands of Ohioans have signed petitions asking Building a Better Ohio to reveal the sources of its funding. “The voters of Ohio—while deciding on which side of Issue 2 they will fall—need to know who is finding the distortions Building a Better Ohio is running other television sets. They deserve to see the list of corporate-backed allies supporting the anti-worker referendum as they make their decision on November 8th,” reads the petition. “The very integrity of our democracy relies on such principles of transparency.”

True enough. But Karl Rove, American Crossroads and Crossroads GPS are not about transparency. Nor is there any indication that Building a Better Ohio will open its books.

Still, the Rove connection is on display this week.

With his criticisms of Rick Perry and Herman Cain, Rove has left little doubt of his leanings in the Republican presidential race. (Rove claims to “have no personal favorite” in the race, but Cain says Rove’s helping Rpmney as part of “a deliberate attempt to damage me because I am not, quote unquote, the establishment choice.”)

As for Romney, he has made no secret of the fact that he would like to enjoy the support of Rove and the network of political organizations that Rove says will spend $250 million in the 2012 election cycle.

So it won’t come as any surprise that Romney’s visiting Cincinnati Tuesday to pump up Republican campaigners for a a “yes” vote on Issue 2—even as the wishy-washy candidate tries to have things both ways by avoiding an express endorsement of Building a Better Ohio’s campaign.

As bumbling as it was, Romney’s was an orchestrated visit, organized and encouraged by the Republican establishment and the corporate infrastructure that sustains it.

Karl Rove has let every Republican know that he is all about Ohio. The question is whether his money and manipulations will succeed in saving an anti-labor law that Rove has been hailing since March—and that has become the top priority of the conservative movement in this year’s election cycle.