You can sponsor their green cards once you have got your US citizenship. I consulted several immigration attorneys and they all said that. The only problem is that they cannot leave US until they get their greencards. Otherwise, they will be subject to that 3 to 10 years' bar. Also notice that citizenship application could be slow for some people due to that stupid name check requirement from DHS. The naturalization process can take anywhere from a few months to a few years. You'd better be prepared for the worst case.
Good luck.