Gov. Ted Strickland likes unions, and unions like a budding fall ballot issue that would give most full-time workers in Ohio seven paid sick days a year.

Yet the proposed ballot issue is giving the governor a headache.

Strickland, a Democrat, began speaking out publicly against the so-called Healthy Families Act last week, urging business and labor to get together and work out a compromise that would keep it off the ballot.

His motivations are both practical and political.

The issue would require companies with at least 25 employees to give workers seven sick days a year, with unused sick time carrying over to the next year. The United Auto Workers, United Steelworkers and Service Employees International Union Local 1199 — which gave generously to Strickland’s 2006 campaign — are pushing the idea.

A recent analysis of the act by the law firm Squire, Sanders & Dempsey obtained by The Associated Press pointed to a number of technical issues within the language that could cause legal problems.

— The act allows employees to carry over unused sick time, but also says that it shouldn’t be construed as requiring employers to offer more than seven paid sick days in a year. How can both be true?

— The act restricts release of information about the employee’s health without the sick employee’s express consent. So could an employer be fined for telling a customer, ‘‘He’s not in. He’s out sick today’’?

— The act forbids an employer from reducing any existing leave in order to comply with the seven-day requirement. What if the employer already offers five paid sick days and two personal days: Would that company be required under the act to offer seven sick days as well as the two personal days, for a total of nine?

Despite concerns of employers, voters love the idea. Therein lies Strickland’s headache.

A recent study by Policy Matters Ohio, a Cleveland-based liberal think tank, found that 2.2 million Ohioans would see their benefits expanded if the measure passes. That’s 2.2 million people who could see a personal benefit in voting for the issue in November.

Voters of both parties support the proposal, but it is especially popular among Strickland’s fellow Democrats.

It has been predicted to drive Democratic turnout in this fall’s presidential race in much the same way a proposed gay marriage ban did with Republican turnout in 2004. As with that issue, the sick-day proposal has national scope: it has been proposed in a dozen states and two cities, and is supported by presumptive Democratic nominee Barack Obama.

Strickland, a longtime Hillary Rodham Clinton ally, has put his support and political might behind Obama since the Illinois senator won the delegates needed to secure the party’s nomination.

He certainly doesn’t want to campaign against a ballot issue that Obama and the unions support and Democrats love. Nor does he want to support a ballot issue that he and business interests views as harmful to his state’s economy.

But Strickland insists, however, that striking a compromise that will keep the issue off November’s ballot will be difficult, if not impossible. He said backers of the initiative already tried.

‘‘We met at the request of the Legislature. They asked the business community and us to sit down,’’ he said. ‘‘It became clear after two or three meetings that they don’t just want it off the ballot. They want no paid sick days (to be required) at all. There just seemed to be no common ground at all.’’

So, for now, Strickland grabs an aspirin and hopes.

Julie Carr Smyth is a reporter for The Associated Press.