Judicial Reports thinks they might. From the article:

As the State Legislature slouched toward adjournment late Thursday with no breakthrough on the issue of pay raises for judges, an infuriated judiciary began to contemplate an escalation in the salary wars.
For many that might mean new or expanded litigation. Some are even whispering “strike.”

New York judges haven’t had a raise in 9 years, and they’re getting pretty pissed about it:

“Judges don’t need to hire lobbyists or public relations people, we need to hire an FBI hostage negotiator,” said Montgomery County Family Court Judge Philip V. Cortese in an interview — distilling the judges’ collective belief that the Legislature essentially held salary negotiations captive to other legislative priorities.

Of course, there are some slight problems with a judicial strike, such as the fact that they can’t legally do it:

Just like the transit workers, judges are explicitly prohibited from striking under New York’s labyrinthine Taylor Law — a statute governing labor organizing of state public servants.
According to Jerome Lefkowitz, chairman of the Public Employment Relations Board, the law treats judges as “management” whose members are not allowed to unionize. At the same time, it prohibits them from striking.
In other words, judges have even fewer options than transit workers or other public employees. “The law says that managerial employees are excluded from the Taylor Law, except Part 210 which says: ‘Thou shalt not strike,’ ” Lefkowitz explained.
In the stern language of that section, no judge can “cause, instigate, or condone a strike.”

So one judge suggested they all just get really lazy instead:

“Another idea is to review all papers submitted very carefully for any errors — typos, misspellings, matters left out — particularly orders and decrees. No handwritten corrections or having your own secretary retype to fix them up. Return them to attorney for correction, and return them again until they are totally correct. Particularly for any firms with legislators in them.”

That sounds very mature, and bound to work.