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:
The orbital ring only requires tethers about 300 kilometers long which is technically feasible with common material like steel, but ridiculously straightforward with better and already available material like kevlar.
There are some important questions. First, how much would it cost to do something like this?
We need to send about 160 million kilograms of material into space (See Birch's boot strap estimates in part 2: orionsarm.com
We also need to include the cost of materials. A space elevator is about 98% steel (though you can use kevlar for the steel) and aluminum, 1% kevlar, and 1% other such as superconducting magnets. Most of the mass (98%) cost around $1/kg, with an average cost per kilogram of no more than about $10 per kilogram.
Summing the above up, we get about $430 billion in launch costs plus another $1-2 billion in material costs.
In other words, we can have a space elevator for less than $450 billion - significantly less than one year worth of DoD spending, one bank bailout, many times less than a variety of pointless wars, etc. This is well within our reach financially in other words.
What do we get in return for this $450 billion investment?
Virtually unlimited value. For example, with a space elevator we can reliably launch our nuclear waste into the sun. We've spent $100 billion building a waste repository in Nevada, but it was ultimately decided not to even use it. Now it costs only a dollar or two per kilogram to get rid of all of the nuclear waste in the world.
Second, we have immediate access to viable asteroid mining industry. Because the cost of delivering payloads to LEO drops to about $1/kilogram, 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.