But he added he believed every Ohio resident would benefit from the tax cuts.
The governor also has opted to support expansion of Medicaid under the federal health care law, providing health care coverage to potentially 366,000 Ohio residents.
Kasich has said he still opposes the health insurance mandate aspect of President Barack Obama's Affordable Care Act. But the decision to expand the federal-state program sets up a potential fight among the governor and Republican lawmakers who are strongly against the federal law.
Bennett declined to say where he stood on it.
Kasich is up for re-election next year. Bennett, asked whether that played a role in the GOP's move to create the website against Democrats, said, "I think we would have done this two years ago if we knew what the Democrats were going to do two years ago. And that is be obstructionists on everything that he proposed."
He said he's concerned Democrats are going to vote against the budget without participating in the process.
"They are just going to be against it to be against the governor," he said.
Some Democrats, including House Democratic Leader Armond Budish, have praised the governor's move to expand Medicaid.
Redfern, also a state lawmaker, backs the idea and said he "absolutely will endorse" it. He said he expects his Democratic colleagues to try to amend the budget to hold a separate vote on the broadening Medicaid coverage.
"Politics is an interesting business to be in," Redfern told reporters. "And to see the rhetorical gymnastics that we've encountered this morning gives even me pause."