Fans and business interests pushing to keep the Raiders in Oakland cleared a hurdle Tuesday when two legislative bodies — the Oakland City Council and the Alameda County Board of Supervisors —approved a nonbinding term sheet for a $1.3 billion stadium plan.

“To me, it’s worth taking the next step because we’re not committing taxpayer dollars to do it,” board President Scott Haggerty said.

Both bodies passed the terms with solid majority support: The City Council approved the terms 7-0 with one abstention, and the Board of Supervisors backed them 3-1 with one abstention.

Under the plan, the city of Oakland and Alameda County would chip in 105 acres at the Coliseum site to the Fortress Investment Group and a development team helmed by former National Football League star Ronnie Lott to build a stadium and parking lot.

The land is valued at about $150 million, and Oakland would allocate an additional $200 million for infrastructure, such as roads, landscaping, lighting and moving a major utility line. The infrastructure portion would be covered by tax revenue generated by the stadium project as well as ancillary mixed-use development.

If the plan moves forward, the existing debt on the Coliseum property, $91 million between the city and county, will need to be dealt with before the property can be transferred.

Supervisor Keith Carson, who voted against the plan, broached the possibility that the city of Oakland, which stands to gain the most from the stadium construction, would buy out Alameda County’s share of the debt.

The effort to keep the Raiders in Oakland had a deep bench at both public hearings Tuesday, with a slew of former players making an impassioned case for the team’s important role in local culture and morale.

“I was lucky enough to play for 16 years. I played for six different teams, and we’ve all played for different teams. But we’re all here, fighting for the Raiders,” said former Raiders quarterback Rodney Peete, who is Lott’s development partner.

At this point, there’s no guarantee the stadium offer will be enough to keep the Raiders in Oakland. Raiders owner Mark Davis has expressed a commitment to move to Las Vegas, which has offered a stadium deal totaling $1.9 billion — $750 million from an approved hotel tax, $650 million from casino billionaire Sheldon Adelson, and $500 million from the Raiders and the NFL.

The Raiders are eligible to move beginning Jan. 1; 24 of 32 NFL team owners would need to vote to approve the relocation.

The specter of failed stadium deals of the past hung over Tuesday’s meetings, raising concerns for some officials and Oakland residents. Supervisor Nate Miley recalled the “tortured history” of stadium negotiations in the 1990s, and several city council members expressed regret for the disastrous “Mount Davis” deal that left the city and county saddled in debt.

Miley was cautiously optimistic about the current plan. Others, like civil rights attorney and activist Dan Siegel, were more skeptical.

“The city of Oakland doesn’t have $350 million to spend on the Raiders,” Siegel said at the City Council meeting, rejecting the mayor and assistant city administrator’s pledge that the proposed deal would not put taxpayer money at risk.

“They’re free to come back on their own dime,” he said, over jeers from dozens of fans in the crowd.

Councilwoman Annie Campbell Washington, who voted to support the deal, said it had unnerved many residents in her district, who feared it would require the city to use critical public funds to prop up a football team.

At a league meeting in Irving, Texas, on Tuesday, Eric Grubman, the NFL executive vice president and stadium point man, expressed skepticism about the Oakland deal, USA Today reported. Grubman said that there was no evidence of breakthrough progress and that the role of private investors made the deal seem similar to previous unsuccessful efforts.

Many speakers, including a number of union representatives who packed the Board of Supervisors meeting, expressed hope that the project would inject jobs and economic vitality into East Oakland.

For many, the emotional stakes are high.

Former Raiders running back Marcus Allen compared the Raiders as a “team with no country” during their Los Angeles stint, because of the disappointment in Oakland.

“I recognize the emptiness, I recognize the pain,” Allen said.

And, he said, “I don’t want to see that again.”

Filipa A. Ioannou and Rachel Swan are San Francisco Chronicle staff writers. Email: fioannou@sfchronicle.com, rswan@sfchronicle.com Twitter: @obioannoukenobi, @rachelswan