If you apply in regular decision(RD)[Deadline: early January] most of the universities reply back to you with a decision by late March or early April. therefore, SATs and Tofel should be taken before January. Although most of her university are flexible on when to receive your results taking them around Jan-February may not be a good idea. It tAkes around 2-3 weeks for your results to be out and it may be too late.
Yes, this is going to be tough but most of the students do this way. You still have 3-4 months so try to manage your time from now. Best of luck.
Also there are some universities that accept applications later than January. Just google them. However, those universities will not be that good. But have a look at them.