That's not at all what they're doing and I'm sorry you've fallen for the propaganda. They are absolutely planning on banning abortion nationally the next time they're in power, they already have the bills written.
It is possible they could without a direct vote. FDA just banned juul for not having adequate studies on effects of their products and how they market them. No vote, not much public discourse. Looking at that in another way they banned a drug/substance that damages cells in your body. Abortions drugs/procedures damage cells in your body. I'm sure if if someone really wanted to at fda they could start requesting abortions federally stopped until they can prove some unprovable concept.
Anything is possible, but I think it's a stretch that they'd use a Federal agency in that way. That would be a big uproar that would guarantee reversal in the next cycle's elections, anyway. Moreover the Republicans complain about the Federal agencies having too much power.
Do you not understand that the "Federal agencies having too much power" is a superficial complaint they use when things work against them, but are happy to flip when it's in their favor?
One easy example, the Trump EPA attempted to ban states from setting their own fuel economy standards via an administrative ruling: https://www.epa.gov/newsreleases/trump-administration-announ.... It also went further banning other states from adopting California's standards for vehicles by unilaterally deciding that emissions rules can't apply to greenhouse gases that are emitted from cars....
https://twitter.com/MZanona/status/1540363376584495104
They also plan on making it illegal to travel to states where abortion will be legal for the purposes of receiving one.