ST. PAUL — The $1 billion Minnesota Vikings stadium bill sped toward floor votes in the state House and Senate on Tuesday, with a burst of momentum that has opponents of public financing wondering how to stop it.

“I would say it’s imminent,” said Democratic Sen. John Marty of Roseville, a longtime critic of stadium subsidies. “I think they have the upper hand, and I think they’re more likely than not to get their stadium within the week.”

The Senate Jobs and Economic Development Committee approved the stadium proposal Tuesday on a voice vote, the latest in a series of unrecorded votes that kept House and Senate versions of the plan on course for floor votes. And it didn’t seem to matter that many lawmakers expressed major qualms about the financing.

At the same time, the committee revised the bill to include more than $40 million to help St. Paul pay off loans related to the construction of the Xcel Energy Center hockey arena and its convention center.

There’s been no shortage of maneuvering to line up votes or otherwise keep the effort alive.

“I do think after a while it starts to take on a little bit of momentum and an air of inevitability,” said Sen. Geoff Michel, R-Edina, who supported the bill in the committee.

In their pricey lobbying effort, the Vikings have help from big business and big labor. The NFL team also has prominent allies in Gov. Mark Dayton and Minneapolis Mayor R.T. Rybak, who have pushed hard for the proposal to rebuild at the Metrodome site.

Critics, meanwhile, oppose the plan for sometimes very different reasons and are scattered ideologically. That’s made it hard to organize pushback, even as stadium supporters start counting heads in anticipation of floor votes soon.

“Those who come up to the Legislature wanting largesse tend to come with a cohesive, united front,” said Sen. Dave Thompson of Lakeville, a stadium opponent. “Those who don’t want us to do this — it tends to be diverse groups of people that aren’t particularly well-suited to the lobbying process.”

Thompson, one of the Senate’s most dedicated fiscal conservatives, and Marty, a liberal, have rare common ground on the stadium subsidy. They both doubt claims that inaction this year risks the Vikings’ future in Minnesota.

The opposition is a patchwork: Critics of gambling, which would provide the state’s money for the project; Minneapolis Democrats who fear an added tax burden if the stadium financing scheme falls short; and fiscal conservatives who dislike the state choosing some private businesses for subsidies.

Opponents also include lawmakers from both parties who see it as a handout to wealthy, successful businessman after several years during which the weak economy forced them to cut social programs and slow spending on other state priorities.

“We’ve been struggling with our budgets the last few years. We’re struggling with, How do we take care of little old ladies in nursing homes?” said Sen. Warren Limmer, R-Maple Grove. “I’m just so surprised we’re tripping over ourselves trying to be the hero to a sports franchise.”

Limmer and others oppose on moral grounds the stadium bill’s expansion of gambling. The plan would let Minnesota charities that operate games of chance to upgrade to electronic versions of some games. The Dayton administration estimates the plan would raise enough every year to pay off construction bonds on the state’s proposed $400 million stadium share. But many lawmakers — even some inclined to support the stadium — are skeptical.

“This financing scheme is literally and figuratively built on a house of cards,” said Rep. Frank Hornstein, a Minneapolis Democrat. He worried that Minneapolis and Hennepin County taxpayers could be left holding the bag.

Hornstein said he thinks most of the 11 House members from Minneapolis, all Democrats, would vote against the stadium bill. That would repeat a pattern from the passage of the Twins stadium bill in 2006, when nearly every lawmaker from Hennepin County voted against the project but lawmakers from greater Minnesota helped deliver winning margins.

“If your own taxpayers aren’t on the hook, it becomes a little easier to support,” Hornstein said.

In a test vote, the Minneapolis City Council voted 7-6 to support Rybak’s stadium plan. The largely symbolic vote adds the mayor’s stadium plan to the city’s lobbying agenda and reaffirms to state lawmakers that Minneapolis has enough support to pass the final legislation, the Star Tribune reported.

Rybak has proposed using existing sales taxes to pay for the city’s share of a new stadium at the Metrodome site. The city’s contribution would be $150 million for construction and $198 million for operations. But the city’s chief finance officer said at a public hearing Tuesday that the city’s contribution will actually amount to $675 million when accounting for inflation, the Star Tribune reported.

It will take 68 votes in the House and 34 in the Senate to pass a Vikings bill. But the plan probably needs at least a few more than the bare minimum so no one could be cast as the deciding vote come campaign season.

Critics have also questioned the process that’s moved the bills closer to floor votes. Backers have tried to avoid hostile committees, and the project is getting more expensive. A provision exempting stadium construction supplies and equipment from sales taxes was removed from the bill, partly to sidestep extra scrutiny from the House and Senate tax committees, which both have strong anti-stadium forces. That raised the stadium’s price tag rises by $22 million, according to the state’s chief finance agency.

Between the circuitous route and unrecorded voice votes even in sympathetic committees, stadium critic Rep. Joyce Peppin questioned what would happen when the bill actually does get to the House and Senate floors.

“The fact that it can’t seem to get through any committee on a roll call vote, can’t make it through if people are going to be put on record, I think is pretty telling,” said Peppin, a Republican from Rogers. “Once you get to the House floor, everybody has to go on record.”