MADISON, Wis.  An increasingly heated national debate about the rights of union workers was stuck in a standoff Wednesday as Democratic lawmakers here and in Indiana stayed away from their Capitols to frustrate Republican efforts to vote on legislation that would undercut collective bargaining and the ability to organize.

While Republicans insisted that the bills were required to balance state budgets, Democrats and thousands of protesters who circled and chanted outside the Capitols in the two states insisted that the legislation was an all-out attack on the middle class.

In Ohio, where thousands of protesters last week had argued against a bill that would ban collective bargaining for state workers, Senate leaders agreed to change the legislation, to allow state workers the chance to negotiate wages. But the measure would now ban public employees from striking.

As the fights in Wisconsin, Ohio and Indiana have garnered national attention, more fights were expected soon  in Oklahoma, where the House is considering legislation that would ban collective bargaining with municipal unions, and in Tennessee, where Republican lawmakers had introduced legislation to prevent collective bargaining between teachers’ unions and local school boards.