Nuclear weapons are
typically designed to detonate in the air rather than on impacting the ground. So when you specify "point blank" I'm going to assume that the explosion is happening above you and you are directly underneath it. If you are flying a plane close to a nuclear explosion, the answer is "no". Even if the colossal blast winds didn't send you into history's least survivable spin, the level of shielding you would need to survive the blast and radiation is incompatible with anything that would ever get off the ground. I suppose conceivably you could create some sort of giant blimp. Can't imagine that going well, either.
But assuming a ground vehicle, then "yes". You specified "unlimited spending". If you throw enough lead and hardened construction material and heat shielding, then you can block any amount of radiation. Multiple cavity layers for shock absorption could also theoretically protect you from the shock wave. A 1MT nuclear bomb (and you can certainly get bigger), yields an initial exposure of 2 RAD. Safe levels are measured in millirads. So you need a protection factor of at least a thousand to get you down to non-elevated levels. I think with lead that's about 4" inches. Concrete is about 24". So sure, it's doable to deal with the radiation effects of a medium nuclear weapon up close. But you're talking about 4" thick lead encasing the occupied part of the vehicle. I don't want to estimate how heavy that would be, but lead is something like three and a half times heavier than pure iron so good luck with that. And remember that your occupied area needs to have sufficient, sealed air supply. And lead itself is not exactly a good frame or shell for a vehicle so you need other parts around that plus the aforementioned cavities otherwise you're essentially sitting in a giant Big Ben waiting for it to ring and liquefy your insides! Also, lead melts at a fairly low temperature, so keep it contained in a steel skin.
So in conclusion, if you're talking unlimited funds and you're happy for your vehicle to be a big dome of steel, lead, and oxygen tanks with very low passenger limit and crawling around with treads like these underneath it:
http://www.theconstructionindex.co.uk/public/assets/diggerblog/2011/07/1310279950_cimg1640.jpg
** Do Not Hotlink images **
then yes, you could build a "vehicle" that could survive. But if you're imagining main battle tanks fighting on under a nuclear rain, no. It would have to be a very, very specialised vehicle and it would move like a terrified tortoise. What you want, I'm afraid, is a bunker. Or better yet, advanced knowledge of where the missiles will strike so you can be very far away.
Disclaimer: all estimates loosely back of the enveloped after a couple of minutes quick googling for amounts of radiation and protection factors.