It takes a majority of both chambers to raise taxes.
McCall said the two measures would be structured in such a way that supremacy would not be required if the state had to pause or change course.
Legislators recently struggled to reach a super-majority to collect certain taxes to pay a raise for teachers.
Some of the loudest critics of the tax cut come from the educational community.
McCall said education needn’t worry about cuts if the measures were passed.
“We also have the funds to invest more in education this year,” he said.
“From the beginning I said we need more taxpayers, not more taxes,” said Governor Kevin Stitt in a statement.
“Lowering taxes on families and businesses in Oklahoma continues our drive to make Oklahoma a top ten state and make it even more attractive for businesses to create more jobs and grow and diversify our economy.”
Emily Virgin, House Minority Chairwoman D-Norman, was asked about the bills during her weekly press availability.
She said the billing process was very flawed and lacked transparency.
Virgin said their caucus has called for targeted, specific tax reform, such as refunding the refundability of the earned income tax credit and creating another tax bracket so that those who earn more pay more.