How to obtain divorce if opposing counsel refuses to respond?

Generally, in every type of proceeding - divorce, property damage, personal injury - there comes a time where one party or another drags their heels in doing something.  Every state has a codified set of laws called Civil Practice or Civil Procedure that allows an attorney the right to ask the court for help in moving a matter along.  Usually this is called Motion Practice.  Most states have a codified Family Law that also provides for the relief you are entitled.

So the answer is "no", you do not have to wait around forever.  Your attorney can actively ask the court for help in moving the matter to conclusion.  This is, however, sometimes harder than I make it sound here.  So be prepared for long court dates and additional legal expenses.