With Wisconsin Gov. Scott Walker maintaining a hard line on his budget bill and Democratic senators refusing to return to Madison to vote, attention is turning to a group of moderate Republican senators to negotiate a compromise to the stalemate that has drawn thousands of protesters to the state capital for a sixth straight day.

The proposal, written by Sen. Dale Schultz and first floated in the Republican caucus early last week, calls for most collective bargaining rights of public-employee unions to be eliminated—per Mr. Walker's bill—but then reinstated in 2013, said Mr. Schultz's chief of staff Todd Allbaugh.

"Dale is committed to find a way to preserve collective bargaining in the future," said Mr. Allbaugh in a telephone interview.

On Sunday, Mr. Walker reiterated his confidence that Republicans would pass their proposal intact.

"We're willing to take this as long as it takes because in the end we're doing the right thing for Wisconsin," Mr. Walker said during an interview with Fox News on Sunday.