That is not at all how the Constitution is set up. There is no explicit power for the executive to ignore the judicial. It has happened once in US history, when Andrew Jackson continued his genocide against the Cherokee after the Supreme Court had ordered it stopped. "John Marshall has made his decision; now let him enforce it!", Jackson supposedly said.
It would be a VERY BAD precedent to do that again. It would be a huge step towards enshrining the President as a dictator.