Well, I don't know what configuration you were planning on (single or double sinks, drawers, doors, etc.), but you could get a smaller standard-size vanity, and use fillers on the left and right to cover what would otherwise be gaps.

If you're ripping down to the studs, could he build it into the drywall to get a bit more space at least on one side?

Can you have open space? Does the cabinet *have* to touch something on both sides?

Some furniture-look vanities don't look good w/ fillers (cabinet-look ones do), but those usually look best if theyv'e got a little air around them.

Sometimes I think it's the space between furniture and walls (and between furniture & floors) that makes a room look spacious. Even if it's 2 inches each side.

And 60" is common--is there no way your GC can help you shave a little bit of dimension off the walls (or something else) to get you an extra 3/4 inch? Maybe that won't work, since 60" vanities are sometimes bigger in the front, w/ the fancy feet, etc. But if you can--can he shave a little off the studs, use a thinner drywall, shift something else over?

There are 54" vanities--but not many, of course

a 56" vanity--$1,000, though
http://www.chansestore.com/q008.html

a 59" vanity (modern style, more extreme than the one below) $900

55" wide, sort of Craftsman looking, $825 (on sale)

Here is a link that might be useful: a contemporary (but not too extremely so) 54 inch vanity $1,000

You might find that many bath vanity cabinets are really only 59" - 59 1/2" wide, planning for a 1/4" - 1/2" overhang on each side to make it a full 60". Check the actual specs for vanity cabinets, you just might need a custom top.

Your issue is very common. I am assuming this is an alcove between 2 walls?

I just did a job which had a 59 inch opening (or 60 inches without drywall). Your cabinet gets ordered smaller than the opening, and fillers are used on the ends. It would be very hard to fit a 59 1/2" cabinet in a 59 1/2 opening. Your alcove would never really be perfectly "square" so you need the wiggle room to get it into place and properly shimmed to level. Like someone mentioned, you can hack away some drywall for extra room. Is you measurement stud to stud?

Do not get the top when you order your cabinet. Many cabinets you get "out of the box" have the tops with an overhang on the edges, and that will not work in an alcove where you are trying to go wall to wall. That should be measured and fit on site after your base is installed.

I would go custom, I would not want to order a standard smaller sized cabinet for an alcove type installation with air spaces around the edges in an opening that small.

Some vendors will do semi-custom, i.e., for a small upcharge on the larger size cabinet, they will make the cabinet to your exact measurement. I know that Adelphi Cabinets will do this. I've had Adelphi Cabinets in my kitchen for 15 years now, and they look as good as new. However, I know that today's upcharge is more than the $3.00 I paid 15 years ago.