Well I am planning to ride to California from Indiana. I was wondering if there are any cost effective bicycle upgrages that may help increase the endurance of the bicycle and or the overall speed.
For speed: clip-on aero bars. You can attach them to pretty much any handlebar.
Why? They offer you an extra position on the bike - that's important if you ride for a long while and your hands / arms / shoulders start to get tired. So you'll ride longer without having to stop. They also allow you to get into a more aerodynamic position, which can help in a headwind. Also, they can be had quite cheaply.
Endurance and speed: An extra bottle holder. If you have to stop to refill your bottles less often, your overall speed will increase. You can get special ones that can hold a 1.5l bottle, not just the regular cycling bottles.
Endurance: Anything that will prevent repairs. Extra-puncture-proof tyres, new chain just before setting out, fresh brake pads, etc. Make sure your bike is in perfect working order before you set out. Any major repairs should be done a few weeks before starting so you'll know they were effective.
If you specify what kind of bike you're riding, I or other people might have more specific suggestions. Since you're asking about cost-effective measures, it might help to know how much you're able or willing to spend.
If this is your first long distance ride, then you should probably do a supported ride. Your friend /spouse in the van would carry spare tires, spare parts, a spare bike, medical supplies, and tools. And lunch or dinner as well as water. They can carry your tent and sleeping bags if you want to camp under the stars.
They'd help ferry you to the next motel if you bonk in the middle of the Arizona desert and give you shelter in a sudden thunderstorm or tornado. They can hit the antique shops or casinos between segments while you're pedaling away.
I can't think of a better (faster, safer) upgrade for a newbie long distance rider.