This author thinks so. Personally, I think that unionization is embedded in the First Amendment, under "the right of the people to petition for a redress of their grievances." After all, if a conservative Supreme Court can decide that corporations are people, why can't the Constitution be viewed as protecting the rights of workers to organize, protest, and bargain for better working conditions?
In other words, I think there is already a civil right to unionize. You can re-write the laws of the land as much as you want--and I think that many of them need to be re-written. I'm all in favor of passing the EFCA, and even amending the Civil Rights Act to protect and strengthen unions. But, until we have more workers who are willing to put there personal comfort aside for the betterment of all workers--not to mention their children--the rights of workers will be little more than words, empty monuments to the better intentions of a rougher but more idealistic age.