I googled the pattern and took a look at it. It is indeed worked in the round. The supplies list says a 16" circular OR a set of double points. I imagine that with the smaller sizes you might be better off using dpns. If the stitches don't fit around the circ, they just don't! You can't really force it to work, and there's nothing more agonizing than knitting in the round on a circ that's just too big for the project. You can also use the 2 circ method or magic loop knitting, videos for both can be found here
under 'Small Diameter Circular Knitting'.