"Apprenticeships lead to good-paying jobs. That would be enough for my Republican Representative to vote against it, although he said otherwise I[n] his campaign and will do so again in his district."
It’s the same old story, davidf, for any position you want to be enacted, you need to exert POLITICAL PRESSURE. To exert political pressure you need RESOURCES. 1. In any given District, you need a Committed Local Voting Block of Significant Size. 2. Articulate & credible spokespersons. 3. Articulate Press Release Writers. 4. A long term Voter Education Program. 5. Money for Lobbying. Personal connections willing to help in any way can be priceless.
You'd best join up with one or more groups committed to an at minimum a generally Progressive Agenda that includes your agenda item. These groups must support an electable candidate likely able to defeat that useless Republican.
Winning one Member of the House will not be enough. At the Federal level the President, House and the Senate must be turned some Shade of Blue.
If you work in a unionized job, try to get active. It may not be easy to get in and may take a while. Once in you may not like the reality of what goes on; that's not the point. The point there is much be learned from the political process on the ground.