It shouldn't (in theory, at least) change much in states without labor unions. This executive order does not "order[] the use of union labor," it simply allows the relevant federal agency to require the use of union labor (and a "project labor agreement" or PLA) on a project-by-project basis, where the agency believes that requiring union labor will "advance the Federal Government's interest in achieving economy and efficiency in Federal procurement . . . "
In theory, at least, in states where union labor is non-existent, this order should not affect much (because using union labor in a state without labor unions could not possibly be economical or efficient). In practice, who knows? As some posters have mentioned/alluded to, it's possible that this could simply put a freeze on federal projects in such states...
The unions can pair this Executive Order with the soon to be passed Card Check legislation to unionize the open shops.
It's all part of a very concerted effort. It's well planned and being executed at many levels through many avenues.
My latest prediction is that TARP banks will be directed to make loans to union contractors only; and TARP insurance companies will be directed to bond only union contractors.
What is going to be done in the next four or eight years will end up taking generations to undue. If it gets undone at all.
Thanks for doing much-needed research for us, Conscience.