There's nothing in the US legal code that creates consequences for disobeying the judicial branch's judgement.
Obeying them is a strong suggestion, and disobeying could conceivably be used as evidence in an impeachment trial, but that's about it.
This isn't a new issue either. It's over 150 years old. Andrew Jackson didn't even get a slap on the wrist for not enforcing the Supreme Court's ruling in Worcester v. Georgia.
Actually, it's one of the fundamental checks and balances. The judiciary has no executive power. The reason a conviction in court sucks for the defendant is because the executive branch actors enforce that conviction by taking the convict to jail.
However the legislative branch pays for those guns (and the men who hold them, the ammunition that goes in them, the vehicles which transport them, and the fuel which powers those).
It's called checks and balances for a reason.
There is no center of power, though the balance may shift over time (and yes, the executive has a great deal of power).
Obeying them is a strong suggestion, and disobeying could conceivably be used as evidence in an impeachment trial, but that's about it.
This isn't a new issue either. It's over 150 years old. Andrew Jackson didn't even get a slap on the wrist for not enforcing the Supreme Court's ruling in Worcester v. Georgia.