It is already possible to build a space elevator. The key idea is the Orbital Ring version of the space elevator, not the geosynchronous tether concept you are familiar with.
See, for example, Paul Birch's writings:
There are many other feasible ways for us to get to space much more cheaply and safely than rockets:
You get the idea. Any of these could be done for $100 billion or less, a negligible cost when considering a GDP of trillions of dollars.
Why do something like this? Overnight, asteroid mining becomes an incredibly profitable industry. Because the cost of delivering payloads to LEO drops from thousands of dollars per kilogram to less than $100 (potentially less than $1) we can now retrieve asteroids with trillions of dollars worth of minerals for mere tens millions of dollars in addition to having an easy viable way of returning those resources back to the surface. We acquire the ability to deploy profitable solar power in orbit above cloud cover and with the ability to return said power back to the surface with near zero loss by running power transmission cables down the elevator.
Just how profitable?
With increased luminosity in space, enhanced exposure time, and the ability to deliver base loads, solar panels pay for themselves in only 1-2 years while having a 20 year life time. In other words, if you put $5 trillion of solar panels into space, you get your $5 trillion back by the end of year two and a $5 trillion income stream each year thereafter. In other words, the US could cut everyone's taxes, both personal and business, income, capital, death, or otherwise, all to 0%, not even cut any benefits or current spending, and pay off the national debt within a decade.
This is the only political issue that matters because it cuts through all the lies. If a politician does have solutions like this, they are stupid or corrupt. They cannot be trusted. It is the perfect litmus test.