Well, it is a bit more complex than that, because of how unions are treated can have an influence on that.
Unions are seen by some workers as the enemy in the US. Maybe corporate propaganda but not as prevalent here.
If they are present, yes they can have an influence. Not usually a governmental issue but even unions can become one.
Sometimes the government sides with the union and sometimes not but to your point it can get complecated.
In Australia, when I was there anyway, unions had a lot more power than in the US.