Governor Pence sent legislators a letter on Monday outlining his plan for cushioning the blow to Jackson and Pulaski counties if the veto stands.
Individual income tax collections were 22 percent lower than expected for the month of May.
The House Speaker says an income tax cut will be part of the final budget.
Governor Mike Pence sought support Tuesday from mayors and local government leaders for his 10-percent income tax cut proposal.
The House Republicans' budget does not include the governor's desired tax cuts, but House Democrats want there to be a vote on the proposal.
The governor-elect's proposal banks on 2.5-percent revenue increases in the next two years and on spending 1.5-percent more in the next state budget.
Tax preparers might have to go back to the 2001 income tax rates, a table that has a lot of moving parts.
A study shows LOIT funding is helping pay for local government operations in Indiana but likely confusing the taxpayers who contribute to it.
Gubernatorial candidate Mike Pence says his plan would save taxpayers in Indiana more than $200 each year.
The state announced recently that it had not distributed more than $205 million in Local Option Income Tax funds.