The problem is not politics, its physics. The Apollo Program was sent into space on a 50 story building made with some of the most advanced metals yet created then filled with high explosives. All that to get about 60-70 tons into space; the "payload" ie the people and the return capsule, was under 2500 pounds when all was said and done. The rocket equation is a bitch that will be obeyed no matter what you want to do. As long as we are using chemical rockets, we are bound to the limits of fuel and engine efficiency. No manner of cash will change the laws of nature. The only way to play with the rocket equation, in a chemical rocket, is to burn lightweight fuel, very hot, and kick it out the back as fast as possible.
The Falcon Heavy will have a max, realistic, payload of 80 metric Tons, limited by the size of the fairing (the part on the nose) and will be closer to 60-70 tons when it starts lofting payloads. these numbers are to low earth orbit, ie where the space station is. To go to the moon, cut the weight in half as the other half of the payload is the fuel to go to the moon. To land? Cut in half again to get a guess on usable payload numbers. The BFR is going to be a massive metal tube full of fuel, with the volume of a 60 story skyscraper, and it is looking, realistically, like a max weight into space of 110-120 tons. (FYI, Musk is saying 300tons to Low earth Orbit and the guys I follow that build working space hardware and engines are all doubting this.) The main benefit is that the rocket is going to be reusable which drops the price per pound to space to something that makes a real space-based economy viable.
To put this in perspective, the Shuttle weighed 99 tons empty. It had a payload of 50-60 tons. It used the most advanced, most efficient engines ever built; they were using hydrogen, as hot as you can get it, sending the exhaust out as fast as it could possible go, and not explode the engines or melt them. Then you had to add in the biggest solid rocket motors ever made JUST TO GET THE THING MOVING. The Solid rocket boosters provided some 75% of the oomph to get the shuttle to orbit. Then you had to deal with the fun and engineering of dealing with hydrogen. Short answer? Liquid Hydrogen is shit to deal with. It seeps into whatever metal you make its container out of, the tanks cannot be reused (unless there has been a breakthrough I am not aware of) and the stuff is so light that you need massive tanks to hold it.
The only way to get more efficiency is to use ion engines, but the thrust is so light you will never get off the ground. Once in space? nothing right now is better. On the ground? Burn some kind of fuel in an engine is the only game in town. If all you need is a gentile nudge and have a lot of time, the efficiency of an ion engine is some factor of 100 better than chemical rockets. The total "delta V" aka change in speed of the Dawn mission, for example, was in the order of 10 kilometers per second which is just not possible with the limits of the current tech.
The modern next-gen rockets are all going to use super chilled, densified liquid methane, which has its own issues. Because methane is much denser than H2 you get more actual hydrogen in a volume, the molecules don't imbrittle your tanks and you can reuse the tanks, piping etc. LCH4 is also much warmer that H2 so you need less energy, insulation etc to handle it. Oh and you can use solar energy on places like Mars to make Methane and Oxygen out of the air and dirt. One tank design was using liquid oxygen pipes as the cooling for the liquid methane, which helps if you want redundant systems to reduce weight. That big tank on the Shuttle Stack? Almost all Hydrogen storage That little, tiny tank on top is the LOX. The problem with methane is that darn carbon atom. CH4 and O2 make water and CO2... if the engine is not hot enough and engineered well enough. If the engine is not engineered correctly, you get a carbon soot covering your impellers, turbines and combustion chambers instead of that CO2 and that causes all kinds of issues. Most of these are being solved now as the main rocket fuel for, say SpaceX, is avionic kerosene which is why the exhaust looks "sooty" on the launch videos. They traded some of the chemical efficiency of the engine for reliability and lower cost. With Methane, from what I have read in the past, the same tricks to prevent soot in the engine won't work because Methane needs higher temperatures and tighter tolerances, and it is harder to use the fuel-rich mixture they currently use to cool the engines and parts.
The Sea Dragon is the largest rocket that I am aware of that had actual design work done on it outside of science fiction. The sound from the rocket was such that everything within 50 miles of the engine bell would be shook to dead or deafened. That rocket had a max payload of 500 tons, on paper-take about 75% of that for the real value. Then there is the cost to pound and do we really need to send a payload that large into orbit any more?
The short answer to your question? 100 tons usable cargo to orbit reliably is doable and a realistic goal; if cash is thrown at the problem, they can make the rockets cheap and reusable reducing the price per kg to orbit. Any more than that is limited by chemistry, physics, and the politics of what you need to launch such a large rocket.