Labor union leaders may have had their fingers crossed, hoping no one would spot the Achilles heel in the self-preservation argument they have used so successfully for many years.

Now it has been called to the attention of U.S. Supreme Court justices.

Government employees have been one of the few bright spots for labor bosses at a time when just 12 percent of workers belong to unions. Given the choice, most people prefer not to pay union dues.

But big labor insists government officials who mandate public employees pay union dues, whether they want to belong or not, are right. Why, where there are public-sector unions, workers who do not pay dues get a free ride at the expense of others, the bosses say.

They do that by enjoying the benefits of collective bargaining funded by dues-paying union members. Or so goes the claim.

Precisely, a group of California public school teachers have pointed out in a lawsuit asking that they not be compelled to pay union dues. It is their suit Supreme Court justices are deliberating.

Not all teachers forced by California to support the state teachers’ union agree with that organization’s collective bargaining goals, the disgruntled educators point out. That means the state is violating their First Amendment rights by forcing them to support causes with which they disagree.

Clearly, they are right, as some justices hinted with questions they asked while hearing oral arguments in the case several days ago.

It is a solid position. If, for example, a group of public-sector workers fear a union’s insistence on higher wages will mean their employer may have to lay them off to save money, why should they be forced to pay dues to pursue that collective bargaining strategy?

Supreme Court justices have little, if any, choice but to agree that is unconstitutional. In doing so, they may be pardoned for pointing out to the unions that in a very real way, it was their own argument that undid them.