Yes, education vouchers are economical and efficient, because education vouchers are ultimately cost effective. Vouchers allow people to use market forces to find better education for their children. Public education is notoriously inefficient. Although it might seem like vouchers take money away from public schools, in the end, public schools will perform more efficiently under the pressure of competition.
Education vouchers open up more choice to families and allow children, especially from low-income urban families. If Democrats and teacher unions are really concerned about these families, they should want to provide more choice. Those in the unions that oppose vouchers do so because they want the status-quo, and they want to keep their stranglehold on education without giving families the ability to choose. Opponents argue that vouchers "drain the money from public education." That's a terrible argument - it presumes that the money "belongs" to the district schools (I distinguish from charter schools which are also public) and that its theirs to lose. Funding public education means providing the funds needed for all children to get the free public education guaranteed to them by the state constitutions, but the funds follow the child. I'm going to say it: If any school (public, private, charter) is not meeting the educational needs of its students, it SHOULD lose resources and SHOULD be shut down. Competition in anything improves the quality of the product. It works for every other sector - how would you like it if you found a great car at a good price but since the dealership is out of your neighborhood, the government will not allow you to buy it there? Vouchers are merely giving the parents their own tax money back, and allowing them to choose a better education for their child. Those in the unions who oppose them are only after their own self interest and union dues.
Education vouchers are just another attempt to privatize schools, which is a horrible idea, but it makes a lot of capitalist money so of course they promote it. If you look at all the countries with the most successful educational systems, they have public schools, teachers unions, massive public investment and spending in education, etc.