The governor has been at odds with the Republican-led legislature over whether to accept federal dollars to cover 275,000 additional low-income Ohioans, as laid out in the Affordable Care Act.
Kasich said the expansion would especially help people with mental illness and addiction who currently can't afford health insurance.
"The ability to get our dollars back from Washington to rehab these people and restore their lives has to be done," Kasich said. "It's just the right thing to do."
With Republican lawmakers unwilling to go along, the governor has taken his proposal to the Controlling Board, which is authorized to accept federal money. Thirty-nine House Republicans, including Speaker Bill Batchelder, have protested the move, and one outside group has threatened to sue if the board approves the expansion.
The controlling board is set to vote on Monday.
"Say your prayers this weekend," Kasich said. "I'm optimistic about this."