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....