I guess "a lot of space" is all relative. Assuming U.S. bills are of a uniform size, (lxwxh), $2,330 in $10 bills would measure 6.1" x 2.6" x 1". (According to WikiAsnwers, a stack of 233 $1 bills is 1" high.) Even at a healthy spending rate of $100/day, that is a 23 day supply of cash, longer as the per day spending amount drops.
In any event, I would carry some ones, fives and tens if/when you think you might be staying in campgrounds, such as BLM, U.S.F.S and state park campgrounds, with "iron rangers." The fees can vary and are often odd amounts. For example, the fee at a BLM camground we stayed at this summer was $6. A U.S.F.S. campground we had planned to use (turned out to be closed) was $13. I'd hate to find myself at a place like that unable to crack a large bill.