They can try, but quite a few state attempts to put restrictions on abortions have been overruled or temporarily blocked by federal courts this year; waiting periods, sonagrams, etc.
The only way to really change abortion law is the SCOTUS. Most everything else that's tried is constantly challenged and blocked or overruled in the lower courts.
The makeup of SCOTUS and federal courts in general will have to become more conservative to ever overturn Rowe and let the states make their own abortion laws.
No single person has greater influence and power regarding abortion in America, than the President of the United States, and head of the Executive branch of government, and it goes far beyond choosing judges.