Speaking at the event across the street from the Statehouse in Columbus, Kasich told food bank supporters on Thursday that he sees a link in their missions to help those less fortunate.
"We've got to organize here soon," he said. "We gotta be over there in that building on Medicaid expansion. No is not acceptable, no is not acceptable."
Kasich is one of eight Republican governors to endorse the expansion despite misgivings about the health care overhaul. New Jersey Gov. Chris Christie became the latest GOP governor to announce his plans on Tuesday. And Florida Gov. Rick Scott said last week he would support expansion.
Asked whether having additional Republican governors on board with the idea would help ease concerns of conservative lawmakers, Kasich told AP, "I think so. Sure."
The governor said he wanted lawmakers to feel good about the expansion.
"We can prevent poverty through this program," he said in an AP interview after Thursday's event. "We can help deal with poverty through this program."
Kasich said he wanted doctors, hospitals and "social service activists" to encourage the Legislature to back the plan. "Go and visit. Tell them what it's about," he said.
Kasich, who faces re-election in 2014, also encouraged the food banks' supporters in his appearance Thursday not to align themselves to a political party.
"Now I'm not telling you to go Republican — that's not what I'm telling you," he said.
"You link yourself to people who care," he said. "If you go into a political environment and you favor one over another, what happens when the one that you favor's not in?"
Ann Sanner can be reached on Twitter at https://twitter.com/asanner .