COLUMBUS — The final tally Wednesday on the $52.3 billion state budget wasn’t the only thing about it that was nearly universal. So was the health insurance coverage it will extend to Ohio children.

Though the Republican-controlled Legislature reined in some of the most ambitious aspects of Gov. Ted Strickland’s initial proposal to cover all 156,000 uninsured Ohio children, lawmakers preserved the bulk of the plan in concept.

As a result, after Strickland signs the bill this week, more poor children will be eligible for Medicaid coverage, eligible middle-class families will be able to buy into the government insurance program for a low premium and higher wage families with children uninsurable through the private market will be able to get coverage.

Ohio joins a growing number of states that have mobilized recently to cover more kids and reach out to children already eligible but not applying.

As of May, 32 states and the District of Columbia had enacted or announced coverage initiatives for children, according to the Kaiser Commission on Medicaid and the Uninsured.

Ohio lawmakers of both parties praised the harmonious nature of negotiations on the budget, which cleared both the House and Senate with just one no vote Wednesday.

In addition to the health provisions for children, the bill expands preschool and full-day kindergarten, freezes college tuitions for the next two years, provides property tax breaks to seniors and the disabled and increases funding for public schools and a special education vouchers.

Sen. Ray Miller, a Columbus Democrat, said the bill also spends nearly $27 million to promote racial equality through investment in inner-city youth programs, mass transit, Urban Leagues and African-American Chambers of Commerce.

Sen. Jeff Jacobson, a Dayton Republican, rebuffed those who criticized lawmakers for ‘‘mindless bipartisanship’’ in order to secure the near-unanimous approval received by the budget.

‘‘People concentrated on what is important, as opposed to people saying it has to be exactly what I want on every detail,’’ he said. ‘‘Because of that, I would argue that the budget can be both excellent and something all or nearly everyone can vote for.’’

Strickland, a Democrat, has line-item veto power over the budget. He said he expects to veto some items but had not made final decisions as of Wednesday.

He said he believes the budget delivers on his promise to insure all Ohio kids, though some families will still have to pay to get coverage.

‘‘It was one of the last pieces of this budget to come together, and I think it is a significant piece,’’ he told The Associated Press. ‘‘For the first time in Ohio every kid can access affordable health care.’’

In addition to the traditional Medicaid coverage available to low-income children, Strickland touted the budget’s expansion of the State Children’s Health Insurance Program to cover children in families earning up to 300 percent of the poverty level, and a separate provision that extends a Medicaid buy-in option to families whose children have catastrophic health conditions that make it difficult or impossible for them to get health insurance on the private market.

‘‘It’s not going to be free,’’ he said. ‘‘These are families that may make quite a bit of money but, because of special needs, their child cannot gain access to coverage.’’

In an extension of those efforts, state Insurance Director Mary Jo Hudson on Wednesday sent out a notice reminding uninsured college students of the state insurance options they have available. The budget also extends health coverage to former foster children.