MINNEAPOLIS — The $1 billion public-private plan to build a new stadium for the Minnesota Vikings took one of its final steps toward reality Thursday, as a slim majority of the Minneapolis City Council voted in favor of a sales tax shift to help pay for it.

A committee comprising the entire 13-member council voted 7-6 to make the city a partner in helping the Vikings replace the Metrodome, putting up $150 million for construction and another $159 million in later operating costs. One final council vote is scheduled for Friday by the same group and is all but certain to have the same outcome.

With Mayor R.T. Rybak pushing hard for the stadium, opponents on the council appeared resigned to their loss. But they used the meeting as something of a last stand, blasting the project as corporate welfare disproportionately funded by Minneapolis taxpayers and arguing that residents should have had a voice in a citywide referendum.

“To me this is a very sad day for our city,” said Councilwoman Lisa Goodman, who said the stadium’s costs to her constituents outweigh its benefits. Goodman said she was ashamed that fellow Democrats, led by Gov. Mark Dayton and Rybak, took the lead in getting the deal done.

Rybak and his backers on the council said it was a good deal for city taxpayers and estimated the project would generate 7,500 construction jobs in the city.

“This is not something that’s all about billionaires,” Rybak said, in reference to team owners Zygi and Mark Wilf. “This is about lots and lots of people who need work.”

The state will pony up $348 million from tax revenue that’s projected to come from an expansion of low-stakes gambling in bars. The Vikings are responsible for $477 million, though much of that is likely to come from stadium-related profits, including naming rights, and a contribution from the NFL.

Minneapolis’ money will be collected from an existing set of sales taxes, which includes a citywide general sales tax, a downtown restaurant and liquor tax and a hotel room tax. The money generated currently pays debt on construction of the city’s convention center. When that obligation is fulfilled in 2020, the taxes will be redirected to paying off stadium debt through 2045.

As part of the deal, Minneapolis will also be able to use another $150 million of those sales tax proceeds to upgrade the aging Target Center basketball arena. Proponents say that will free the city of much of its ongoing financial obligation to Target Center and result in property tax savings for homeowners.

But stadium backers on the council spent more time pitching the creation of construction jobs to an audience of hard-hatted construction workers that filled council chambers during the more than three-hour meeting. Influential unions pushed hard for the stadium plan and were pivotal in lining up council support at a time when it appeared Rybak was having trouble assembling a majority.

“I don’t like making rich guys richer,” said Councilman Don Samuels, who represents the city’s economically challenged north side. “But in this case, while the rich get richer, the poor will get richer too.”

Councilman Gary Schiff said the jobs will come at a steep cost to the city’s taxpayers. If 7,500 jobs are created, he estimated, the city’s total contribution would be about $90,000 per job.

“I just think this is a deal that generations to come will criticize us for,” Schiff said.

Dayton and Rybak will soon appoint a five-member “stadium authority” to get the project rolling. Actual construction, at the current Metrodome site, is not likely to get under way until spring of 2013.