Yesterday I noted that the Obama campaign is seizing on Mitt Romney’s strong support for the Ohio initiative rolling back public employee bargaining rights — which was soundly defeated on Tuesday — to bolster its message that Romney can’t be trusted to safeguard the economic security of the middle class.

The presidential race is a year away. Is there really any chance that Romney’s stance on Issue 2 could matter to his chances in Ohio?

We don’t know. But here’s a new data point. The AFL-CIO has released polling it conducted among those who voted on Issue 2. Check this out:

As you may know, Mitt Romney has said that he strongly supports Issue 2. If Mitt Romney is the Republican nominee for president next year, will his support for Issue Two make you more likely or less likely to support him?

More likely to support 19

Less likely to support 49

No effect 24

Nearly half of those who voted say they’d be less likely to support Romney due to his strong support for Governor John Kasich’s law rolling back bargaining rights.

A few caveats. This poll was conducted by a Dem firm for an interested party, though polling guru Mark Blumenthal is vouching for their transparency. Obviously these numbers are inflated in comparison with the broader Ohio electorate, since only those who voted on Issue 2 were polled, and it was resoundingly defeated. This could be measuring current passions, which will have cooled considerably in a year. Many other concerns will drive the presidential vote.

But the poll does suggest the possibility that a sizable number of voters who opposed Issue 2 could view Romney through the lens of their distaste with the overreach the measure embodied, and perhaps be somewhat influenced by Romney’s support for it.

Indeed, in a particularly telling finding, 53 percent of Issue 2 voters said Kasich and Ohio Republicans were pursuing the measure out of a ”partisan agenda to weaken labor unions,” rather than because they were interested in government efficiency. In other words, voters grasp the ideological nature of the GOP drive to roll back public employee union power. That dovetails with the Obama campaign’s message about Romney and Ohio, which is that his support for the measure demonstrates ideological hostility to policies that will fortify the economic security of the middle class. So maybe Tuesday’s outcome will matter to some degree next year to the outcome in a state that has historically decided presidential elections.

UPDATE: One other point: A majority, 57 percent, also said Republicans backing Kasich’s law are putting the interests of big corporations ahead of those of average working people, which also seems to dovetail with the Obama message about the meaning of the vote and Romney’s support for the initiative.