Playing a game of political chicken, Democratic senators who fled Wisconsin to stymie restrictions on public-employee unions said Sunday they planned to come back from exile soon, betting that even though their return will allow the bill to pass, the curbs are so unpopular they'll taint the state's Republican governor and legislators.

The Wisconsin standoff, which drew thousands of demonstrators to occupy the capitol in Madison for days at a time, has come to highlight efforts in other states to address budget problems in...