My "student" tried to make this blanket. She tried it on straights; all of the sts fit, but it was a tight squeeze. I recommended from the beginning that she should use circs since the yarn is bulky, but she was too "afraid". There's no reason to be afraid I told her as much too!
Anyhoo - you don't have to knit a big circle to use circular needles. When you've completed one row, you simply turn your work as if you were still using straights. Simple
Hope that helps!