ST. PAUL — After hours of debate, the Minnesota Senate approved a bill late Thursday night that will make major changes to the state’s health care system to conform with the Obama administration’s health overhaul.

Lawmakers voted 37-28 to pass the measure, which implements the health insurance exchange, an online marketplace for 300,000 uninsured Minnesotans and others to shop for coverage plans and seek assistance to pay for them. The debate stretched late into the night as Republicans in the minority failed to force changes to a plan they consider too expensive, too intrusive and lacking in accountability in how the exchange is governed.

“This whole bill is about taking away something that’s working and replacing it with a big gamble, in Gov. Dayton’s words,” said Senate Minority Leader David Hann, R-Eden Prairie. He was quoting the DFL governor’s description in a radio interview earlier in the week; on Thursday, Dayton again referred to the size of the undertaking, calling it “gargantuan.”

Under the federal health care changes, states must either design their own exchanges or let the federal government handle the job. Minnesota lawmakers are working on a federal deadline to have exchange legislation passed and signed by Dayton by the end of March, looking toward an Oct. 1 start to enrollment.

In addition to aiming to provide coverage for 300,000 uninsured people, the health exchange could cover another 600,000 now on government coverage plans and another several hundred thousand people who work for small businesses that it’s hoped can get better deals on insurance in the exchange.

“This is a website that will allow for the first time real apples-to-apples comparisons between insurance plans,” said Sen. Tony Lourey, DFL-Kerrick, the bill’s chief Senate sponsor.

Backers have said the website would be similar to airline ticket clearinghouses like Expedia, will be governed by a seven-member board appointed by the governor and subject to approval by the House and Senate. It’s projected to cost $60 million to year to operate.

That’s a key difference between the Senate bill and a companion bill the House passed Monday. The House bill funds those operating costs with a tax on exchange premiums up to 3.5 percent. The Senate wants instead to fund it by diverting money from an existing 75-cent state fee on a pack of cigarettes.

Another key difference between the two bills is a provision in the House bill meant to entice insurance companies to offer their plans on the exchange by letting them sell some of their specific products — an inclusion opposed by some of the Legislature’s more liberal members. That provision is not in the Senate bill.

Differences between the two bills will ultimately have to be worked out in a conference committee.