In the US most employment contracts are at will. This means that you can leave the contract at anytime. The majority of the contracts I have been on had a clause that requested at least 2 weeks notice, but generally the primary penalty for failure to give notice was no longer being eligible for rehire.
My experience has been that after a normal time period(6 months - 1year) you can request a rate review and generally receive a bump in pay if there is room between your rate and the companies break even point. In order to make the best case for this I do my best to keep in contact with my recruiter, and manager at my home company. Having them on your side when you request a bump is always a plus. In addition they will know if it is possible or not.
I would try to get to a rate where you feel comfortable committing for the entire length of the contract at that rate. If expenses increase while in your contract explain that to your company. They are businesses, but they are in the business of managing people. If the company gets a bad reputation for misusing its contractors that is bad for their business. For this reason, generally, contracting companies build in a buffer so they can give you a pay bump, or other benefit to help keep you happy. If their customer(the people you are contracted to) see that their employees are struggling to survive it does not look good upon your company. It is good business to keep you happy.