ST. PAUL — Every school district in Minnesota would get state funding for all-day kindergarten under an education finance bill that was approved late Tuesday by the state House.

House Democrats made education their marquee issue for this budget year, and top lawmakers said their focus on early learning was the key to improving a growing achievement gap and education as a whole.

Several Republicans questioned whether that investment would deliver. But after hours of debate and unsuccessful amendments to give school districts more flexibility on how to use all-day kindergarten funding, several Republicans joined Democrats in approving the bill. It passed on an 83-50 vote.

The bill increases education spending by $550 million compared to the state’s last budget, when the Legislature was controlled by Republicans. Coming in at $15.7 billion, it consumes about 40 percent of Minnesota’s total proposed spending.

“We’re putting dollars in areas that we know, and in areas that we know have a proven track record in improving student performance,” said Rep. Paul Marquart, the bill’s author and chairman of the House Education Finance Committee. On top of fully funding all-day kindergarten starting in 2014, his bill boosts early learning scholarships for poor 3- and 4-year-olds by $50 million.

“By starting out early … we are going to get every single child to the starting line at the same time.”

The House budget adds $209 per pupil to the state’s bedrock funding formula, which would bring it to $5,433 per student. House Republicans voiced support for that increase and other measures in the bill but argued that the state should use more new money to add to the general formula rather than tie it to specific programs such as all-day kindergarten.

Rep. Kelby Woodard, R-Belle Plaine, moved to give school districts more flexibility in using all-day kindergarten funding, “so that they can decide where the best use of this money is,” he said. His amendment failed.

Democrats have stressed that individual districts can choose not to offer all-day kindergarten. Those that opt out won’t get the state funds dedicated to that programming. About two-thirds of the state’s school districts currently offer all-day kindergarten, but many of them charge for it. Lawmakers expect the funding will extend all-day kindergarten to 59,000 Minnesota children.

Marquart’s ultimate goal is lofty: 100 percent early reading rates and 100 percent graduation rates by 2027, when next year’s kindergartners will graduate from high school.

To that end, his bill adds six more regional centers throughout the state to help districts set plans ensuring schools are on track to improve graduation and reading rates, and follow up if they falter. There are currently three such centers, which focus on struggling schools.

House Republicans argued that is enough to help schools meet Marquart’s goals. They offered several unsuccessful amendments to shift money away from the centers, instead shuffling that funding to the state’s early learning scholarships or reduced-price lunches.

“The accountability comes with test scores. More government bureaucracy does not produce the accountability the public wants to see,” said Rep. Glenn Gruenhagen, R-Glencoe.

The bill also retools the state’s high school graduation exams, replacing the current score-based graduation test with a system that Democrats say will help struggling students earlier and better prepare all students for college.

But Republicans said removing the minimum score that students need to exceed to graduate goes too far. Several members wore buttons on the House floor that read: “Don’t dumb down the diploma.”

“Students need to know that a diploma counts for something,” said Rep. Sondra Erickson, a Princeton Republican and retired English teacher.

Decrying the current “high-stakes” testing approach, Democrats defeated several Republican-backed efforts to re-insert some scoring provisions into high school graduation exams.

Unlike the Senate’s education spending bill, House Democrats’ tax plan will pay off about $850 million in IOUs to schools that the state used to balance previous budget deficits. Legislative leaders have been split on that issue since the start of session.

“We told Minnesotans we were going to do that, and Minnesotans want us to do that,” said House Majority leader Erin Murphy, DFL-St. Paul. The House is expected to take up its tax bill Wednesday.

The Senate bill also focuses on early learning programs, but only adds $52 to the bedrock school funding formula. Senators are expected to debate and vote on that bill on the floor later this week. Once both proposals have passed, lawmakers from both chambers will iron out the differences between their bills before sending the final version to Gov. Mark Dayton for his signature.