That's a bluff. They have to live with the Hyde Amendment now.
No doubt they would like both government control of health care and overturning the Hyde Amendment.
They will not jeopardize getting government control of health care. And anyway they will get taxpayer-funded abortions as well because an executive order on this topic would exceed presidential authority and would be nearly meaningless.
I mentioned this up thread, but the Senate Bill, in its current state and even with the continued enforcement of the Hyde Amendment, will still provide federal money to pay for abortions. How? Because this H.R. 3590 includes provisions that will allow for subsidies to be paid to people to help them (meaning, pay for entirely) their private health care insurance.
This EO specifically states that it's not to be taken as a prohibition on subsidies paid to private insurers who offer as part of their coverage, elective abortions. And, neither the Hyde Amendment, H.R. 3590 nor this EO disallows federal funds to be paid to state health care plans that cover elective abortions.
It's complete smoke and mirrors. The great lion's share of new people getting health care coverage are going to be getting private insurance paid for by public money - your tax money, and my tax money.