That old Archimedes quip about a big enough lever is largely accurate, give me unlimited resources but only modern tech and moving a spaceship to Mars is minor, we could move the whole damn solar system by suspending reflective statites over the Sun.

If we could afford to throw a few megatons into LEO, and we technically can though there are better things to do with the money, then yeah, we can "Get your ass to Mars", so to speak. Radiation shielding, supplies, all of that is just about mass. Take Radiation Shielding, that is about area, but mass is about volume. So a cylinder budgeted to have only a tenth of its mass as shielding has a lot better shielding if it is twice as wide because it can hold four times the stuff and only needs double the shielding. Hell, give me a cylinder 100 meters in radius and we won't even have to worry about health effects of weightlessness, we can spin it twice a minute and have half earth gravity to get them used to lower Martian but with minimal health issues and that's wide enough to avoid the problems associated to spin-gravity. So yeah, with a big fuel budget the technical issues aren't only not a problem but actually a lot smaller.

But fuel is an issue, because it cost us around ~$10,000 per kilogram to get to LEO and that means ferrying up a megaton, around a billion kg, would cost us around 10 trillion dollars. Is it doable? Sure. Do we need a full megaton? No, hardly, and that's where the problem arises. Every time we shave off mass to shave off cost we increase those 'technical problems'. It's like building a mile high skyscraper. Can we do it? Sure, absolutely. Should we with current tech and situation? Hell no. Even if people gave the thumbs up to a trillion-dollar expedition, which is what I'd want to do it, I'd still say no. A Mars colony is an utter waste of time until we get better tech, and a trip to Mars for no other purpose but to plant the flag is stupid. Until we jump some more technical hurdles.