Republicans are just opposed to anything that involves a government. Ignore them, or find yourself in a world where nothing gets done. Some projects require serious heaps of cash on a very long-term investment for the public good. Exactly the sort of thing governments are for.

Building rail infrastructure, much like building roads, is a costly thing to do. But once built, it lasts a long time with minimal maintenance costs (compared to building the system). So you don't have to recoup all that money in five years or so, you can easily take fifty or even more. If you do it right, trains can take literally thousands of people on at the same time without breaking a sweat. So you have a lot of passengers paying a fare to get to where they need to be. Make using the train more convenient (keep the TSA away) and preferably cheaper than using alternatives (plane, car, bus) and you have a winner. Electric trains are cleaner too, so for many governments it's a good idea to invest in rail infrastructure for that alone.

In my country of ~17 million people, every day on average 1.1 million people hop on a train. Because for the 6.5% of the population that takes the train every working day (the highest in the world, I'm told) it's a better option than whatever alternative they may have.