update
So this is an update, just in case anyone else runs into this same sort of problem. When I had called in, the manager said that he would "see what he could do." He had a meeting with the owners of the company and would get back to me Monday which was exactly 4 business days after I had signed the contract. Coincidence? This was before I knew about the possible 3-day cancellation law.
Most states have a 3day period in which you can cancel a contract. In Connecticut this only applies to certain contracts (automobiles, timeshares,etc). It's called the "Cooling Off" period. I'm not sure if this law applied to my case because it was a contract for a private travel club that deals with timeshares, but I thought I'd give it a go anyways.
The intent to cancel must be received in written form. You cannot simply say I told them over the phone. To cover all my bases, I sent them certified letter with return receipt, notifying them of my intent to cancel and also stating that I was going to report them to the Connecticut Consumer Protection agency and BBB if they didn't respond to my letter within 1 week. The next day, I went to their office with the same letter in hand, had the receptionist sign a form indicating that she had received the letter, and then talked to the manager. At first he was rather rude, but then he asked me what I intended to do, was I ready to take legal action? I said yes. All of a sudden, he became rather nice and genteel. To make a long story short, they ended up cancelling my contract and I received a full refund.
So I'm still not exactly sure if the 3-day Cooling off period applied to my case since it was a company that dealt with timeshares, but may not have exactly been a timeshare company. Here's a link to an AARP page with good info regarding contracts.
http://www.povertylaw.org/legalresearch/hotline/ct/52639B.htm
I had sent a copy of my contract to a lawyer friend though and she said there were several things wrong with the contract (but I did not know this until after I had already confronted the manager). Anyways, so if you find yourself in a similar situation, there's no harm in trying to cancel. Worst case scenario is that you find yourself stuck in the contract, which would be what have happened to you if you didn't do anything.