MADISON, Wis. — To end a high-stakes stalemate over union rights that has captured the nation’s attention, a handful of Republican lawmakers in Wisconsin might have to stand up to their new governor.

Gov. Scott Walker made clear Monday he won’t back off his proposal to effectively eliminate collective bargaining rights for most public employees. Senate Democrats who fled the state last week to delay the plan vowed not to come back to allow it to pass — even if they have to miss votes on other bills Tuesday. And union leaders said they would not let up on protests that have consumed Wisconsin’s capital city for a week and made the state the center of a national debate over the role of public employees’ unions.

That dynamic means it might take Republicans in the Legislature who believe Walker is going too far to try to break the impasse. One idea that has been floated by GOP Sen. Dale Schultz would temporarily take away bargaining rights to get through the state’s next two-year budget, then immediately restore them.

While it’s unclear whether that would be acceptable to his colleagues, Democratic Sen. Jon Erpenbach said in a phone interview from the hotel room in Chicago where he’s hiding out that Schultz was brave for making the proposal. He said Schultz, of Richland Center, and five or six other Republican senators who have ties to organized labor are in the best position to get both sides to negotiate a deal.