The Democrats have fled the Wisconsin capital to avoid an upcoming vote to deny collective bargaining rights to government workers. I think the Democrats are right but probably for a different reason. The first amendment (supposedly) protects free speech and the right of the people to peaceably assemble. A union is, at its core, a group of people exercising those rights. The fourteenth amendment applies the first to the states -- really, the Supreme Court applied the first to the states, but that's another discussion -- so in my mind, an attempt by the government to bar unions is unconstitutional (keep in mind that I'm no lawyer).
In the particular case of Wisconsin, and really governments in general right now, government incomes are falling (unemployment) and expenses are rising (healthcare, welfare, etc.). Like a business, they need to cut costs, raise revenues, or declare bankruptcy. The latter two are politically untenable, which leaves cost cutting. Hence, the governor wants to cut workers' salaries and benefits. The union is simply trying to prevent that. I'll let you draw your own conclusion about whether or not the union is in the right.
I'm willing to give the Democrats the benefit of the doubt and assume that part of their reasoning in leaving the state was defending constitutionally protected freedoms, as I described above, but I believe much of it to be predicated on the pro-worker position(s) of the Democratic party and the idea that the government workers in question deserve "fair" compensation. The idea of "fair" compensation is murky, at best, when dealing with governments, though. There's a tendency to compare government salaries to private sector salaries and assume that they should be similar (at least) in the cases where the job functions are the same. If government salaries are too low as compared to those in the private sector, government can raise taxes to raise its workers' salaries. This would likely have a negative effect on private sector workers, though, as they would see less "take-home" pay, and employers may even begin to pay less as well. As private sector salaries decreased, government could lower its workers' salaries and, in turn, taxes. In theory, this would reach equilibrium at some point, and we could all claim that "the market works". (Also, keep in mind that I'm no economist.)
In reality, this would probably never actually happen because the union would fight tooth and nail to prevent the government from lowering its workers' salaries, much like what is happening now. The other problem is that it's not the market at work. In a truly free market, people would determine the workers' salaries indirectly by voluntarily paying for the product produced by the workers. The government isn't subject to market forces, though, because its revenues come in the form of taxes. People, in general, don't pay their taxes because they want a product that the government produces; they pay them because the alternative is prison.
I don't mean to sound anti-union; I'm not against them, per se. Like anything else, they can be good, and they can be bad. For interested readers, Henry Hazlitt gives a much fuller and better treatment of the subject.