Between Catskills, Millersburg, Page County, Washington County, Killington, and a whole slew of others I've missed, stage racing season is on the serious wane. However, there's still the granddaddy left to go, and since Green Mountain is the one I'm doing this year, it's the one that counts. Stage races (and travel cross weekends like Nittany and Gloucester) are generally time- and resource-hungry beasts that you've put a lot of training and focus into. You don't want to let a stupid mechanical throw it all to waste.
First things first, your bike should work absolutely perfectly before you even leave, and in order for that to happen you need some foresight. As every stinking thing on your bike gets more and more specific and specialized (lower case "s"), it gets harder and harder for shops, even big ones on the internet, to keep stuff in stock. Check everything from tip to tail, and if it doesn't work perfectly, address it now while there's still time.
If you don't do your own bike work, you are going to need to give your preferred shop some time with your bike - it is after all summer, when they do like 80% of their business for the year and mechanics are being asked to do ridiculous things like work 12 days straight without a day off. See if you can book an appointment for your bike, in order to minimize the time when it's sitting in the shop with you not training on it. Let them know in advance what you want worked on/replaced so that they can have the needed parts.
If you are the type to do all of your bike work, time is money. There's no better way to wind up overpaying for stuff that's not exactly what you wanted than to wait until the last minute. Survey your bike completely and order any parts that you are going to need, leaving as much time as possible to deal with stockouts, shipping, etc.
Even if you are completely inept at bike work, chances are that someone you're traveling with will be able to help fix any disasters that occur during the trip. The key is to be prepared and have enough spares to address as many mechanical incidents as you can. I like to bring the following tools and parts for a weekend of racing...
Full hex key set (1mm to 10mm)
Channel lock pliers
Chain whip and lock ring remover
Channel lock pliers
Needle nose vise-grips
Chain connector link
Set of brake pads
One of every spoke length that's on wheels I'm using
Spare brass nipples
Pair of skewers
Various M4, M5, and M6 bolts
Two brake and two shifter cables
Brake and shift cable housings, end caps, and crimps
Disc rotor (if you have disc brakes)
Bar tape (it always gets wrecked in a crash)
Pedals and cleats (old and imperfect but operational)
Derailleur hanger (www.wheelsmfg.com is THE place to get them)
Bike cleaning supplies
Pit wheels with tires you'd willingly race a crit on
All of this is things you'll use eventually anyway, so it's not like there's any extra cost for doing it. It doesn't take up much space in the car. And as we all know, Karma usually spares us any eventuality for which we are prepared - the more stuff you're prepared for, the more stuff you'll avoid!