Congress almost certainly does not have the power to ban abortion due to the tenth amendment. The supreme court ruling that the constitution gives no right to abortion means the power to create legislation about abortion is no longer granted to congress, which means it's reserved to the states under the tenth.
This seems a little naive considering Congress has found plenty of ways to coerce states into implementing laws (national speed limit which was later repealed, national drinking age, etc.) by threatening to withhold funding and these laws have stood up to a tenth amendment challenge. Similarly the GOP could threaten Medicaid funding for states if they don’t restrict abortion, which would be disastrous for the state and thus impossible to ignore.
National Federation of Independent Business v Sebelius disagrees. I believe all the highway funding stuff worked because they could claim interstate commerce.
In the case of Medicaid funding, I thought the outcome of that case was that the Federal government couldn't threaten existing Medicare funding but it was allowable that any future Medicaid expansion be denied to states if they didn't comply with the ACA. The makeup of the court has changed since then though and in general the conservative portion of the court did generally vote to say that coercive use of federal funding was unconstitutional, so hopefully that remains the same when the ideological nature of the case is reversed.
