The bill makes cuts in several programs, reduces aid to local governments and calls for issuing millions of dollars in additional bonds to pay for highway projects.
Graves says tax increases are needed to adequately fund state programs and give schools more money.
House approval of the plan came on a voice vote. A final vote is expected today. Earlier Thursday, Republican leaders delayed Senate debate on its version of the budget when they could not get commitments for the 21 votes needed to pass it. However, both the Senate and House have sent strong signals that they will not approve tax increases, as Graves proposes. On Wednesday, the Senate defeated a school finance plan that raised sales and inheritance taxes.