Oxygen is easy -- import/manufacture more and fill your atmosphere with it. The hard part will be in getting the atmosphere to begin with; if you can do that, the rest is just details.
But here's the problem with a Martian atmosphere: Gravity. More specifically, Mars doesn't have enough of it.
Martian surface gravity is $3.711\;\mathrm{m/s^2}$; that's only a hair under 38% of Earth's $9.78\;\mathrm{m/s^2}$. If you were to take Earth's entire atmosphere and transplant it onto Mars, it would quite simply weigh less, and you'd end up with a surface pressure of approximately 38 kilopascals (compared to Earth's ~100 kPa)1. At that pressure, water would boil at 75C at the surface (versus 100C here on Earth). So you'd have to keep the A/C cranked pretty high just to keep your oceans from boiling off! I can't speak to the other effects of such a low pressure (you're going to have all the effects of acute "altitude sickness" until you acclimate, if you even can acclimate to an Earth-equivalent altitude of ~25,000 ft...), though it seems to me that that would be extremely uncomfortable, to say the least.
But there's an even bigger problem: Mars doesn't have enough gravity to keep that atmosphere. Mars' low atmospheric density is not merely a random happenstance; gassses have a tendency to float away. This is even true of planetary atmosphere, which can escape into space. Mars is simply physically incapable of sustaining Earth's atmosphere, so your 38 kPa atmosphere is going to get even lower, which will drop your boiling point lower still; eventually you're going to end up right back where you started, with a 600 P surface pressure. (Note that I believe it will take a very, very long time to get back to this point, but you will lose a lot of atmosphere quite quickly, with the losses slowing down as there's less to lose.)
Is there any way to make Mars livable at all? You'd pretty much have to construct a solid bubble, or some kind of protective shell at least, around the planet to stop the outgassing. And probably have to make it a pressure vessel so you can actually artificially pressurize the planet just like you would a spacecraft. If cost is truly no object, this could certainly be done, except that I'm pretty sure it's out of reach of modern science -- I don't think we have materials, let alone construction methods, capable of building something on this scale, even ignoring the airlocks necessary for spacecraft to reach the surface. And the raw materials! Even ignoring how much money you spend, you're going to have a very hard time just getting the materials to build something of this scale! You'd be much better off just building luxurious domes around your Martian colonies: same result, but on a scale that's at least marginally feasible.
Edit: TimB in the comments below points out Venus, which has about 91% of Earth's gravity, yet a surface atmospheric pressure of around 92 times that of Earth (9.2 MPa)! I don't know what allows Venus to hold onto that much atmosphere, however I suspect the reason is that Venus' atmosphere is primarily composed of much heavier elements than Earth's; for example, Earth's atmosphere is nearly 80% nitrogen, which has a molar mass of about 14 g/mol, whereas Venus' is over 96% carbon dioxide with a molar mass over 44 g/mol -- more than 3 times as heavy, and composing 1.2 times as much of the atmosphere!
Which brings up the possibility that if you could find a gas that's safe for humans to breath (and mixes fine with the oxygen) but weighs significantly more than nitrogen, you could potentially solve the problem of obtaining a higher atmospheric pressure by simply creating a heavier atmosphere!
1 There's a significant caveat here, and that's that I could not find any direct corroboration of my assumption that surface pressure would change in direct proportion to surface gravity. However, planets are not pressure vessels; what you feel as "air pressure" is literally the weight of the atmosphere above you being pulled down by gravity onto you. Thus I believe it is a more than reasonable assumption that 38% gravity means 38% air pressure. On the other hand, with less pressure, the gasses will spread out further, which means the outer reaches will get further away and be affected by the inverse-square law; the upshot of this is that my numbers may be too high, making this even worse for plausibility!