There shouldn't be any additional fees for taking out, nor should the car dealership object to your putting a down payment on your credit card.
Why wouldn't you just wait though until you have the check in hand and then go ahead. Almost all dealerships aren't going to miss out on a sale because of a few days.
Starting Score: 627 EQ, 621 TU - 11/15/08They will always have a car you want, if not they will get it. So don't be pressured to buy quickly just because of that. Impatience sounds like the biggest thing.
If you take out a larger loan, then yes your monthly payments will be higher than if you took out the smaller loan. Even if you send in a very large principal payment, you will continue to have the higher payment each month. The other option is that you send the payment to apply towards the upcoming payments, and start banking that money so you have extra savings when it comes time to start making payments again. This will cost you a lot more in interest though. Remember that car loans are simple interest.
The first dealership that I went to that had my dream car (2009 Ford Escape, black with tinted windows, and a sunroof) was a waste. They came down $900 off the asking price but it was still way too high after they added in fees and such. They even ran my credit and came back with cap1 at a HIGHER rate (my offer was 8.85 they came back at 8.90- he had the nerve to say "same thing" when I pointed out my rate was lower 
). Needless to say, I walked away. They left me with such a bad feeling and I literally felt like I had been in a fight and lost. Old school cars salesmen who want to take advantage of a woman alone and act like they are cutting me a deal. He called the next day and I was trying to get the break down of the costs again to see if I could drop some things (like the dealer offered extended warranty, and just buy mine on my own) but the guy was purposely vague when I asked for amounts. I got frustrated and told him thanks but no thanks, I was on my way to see another car and they were still asking way too much....
The second dealership was a DREAM to work with (2010 Jeep Compass, black, low miles and a certified pre-owned). I saw the car online, sent an offer via email, they accepted broke down how much I was paying for everything, went and test drove. Presented my check and they asked about interest. I told them for the year of the car, it would be 8.25. He said he was fairly certain he could get it lowered, and plus if I used the check I wouldn't be able to add in my GAP insurance. Went ahead and let him run it, and I came back with a cap1 at 7.85!! Paperwork signed, truck washed and a full tank of gas later, I was off! 
They didn't even bat an eye when I said I needed to put the 3k on my zync! The finance manger even joked and said oh no it said declined- and I must have practically soiled my pants- and he laughed and said just kidding and started talking about how Amex cut his card off on his honeymoon. I have run up to 10k through my card in a month and paid it off, so I knew 3k wouldn't be an issue. I was going to check my spending ability before I went up to the dealer but it was so last minute I forgot. The whole experience was great! I left my license in my jeans from the previous day at the other dealer and they still let me buy the car, I faxed them my license this morning! I got a great deal. a great car, and I wasn't stressed out when i left! I was determined to have my payment as close to $200 as possible- and I got it to $217!!
So here I sit with my new car, piece of mind and an extra 3000 points on my card!