Shimano 600 front brake and the wheel set is from a Bianchi Pista. I can get it in my VW Golf believe it or not by taking off the front wheel. I can open the brake up enough to squeeze the tire through it but it's a real tough fit and getting the wheel back on last time resulted in the brake moving and slipping and taking off a little paint. Any idea on what I can do other than setting the brake wider? Any wider and I'd be using the entire pull of the lever to brake.

What size tire are you using?

Just deflate your tire a little bit when removing/replacing it...

If your brake lever has a quick release on it that will give a bit more latitude.

600s should have a quick release lever where the cable clamps in (mine do, anyway). The up / unlocked position should give you plenty of room - I can extract 32mm touring tires from mine with no drama. Are you running your brakes super tight or something?

Also, B-R-A-K-E-S.

you could always adjust the brake with the barrel pulled out of the lever or caliper a little bit. screw it in to get some slack when you need to take the wheel off.

- assuming you're somehow not getting the clearance you need after releasing the qr lever...

Was the QR in the open position when you set the cable tension? Thats all I can think of.

I think the problem is definitely how I set up the brake. When I install the cable, I want the barrel screwed all the way in right?

yes

You don't have to.

You can have it set just enough so that you can screw it back in to have it clear the tire. In which case you lose the convenience of having that barrel adjuster to account for the full range of brake wear but it's a compromise.