There is no basis in the Constitution for President's authority to do this.
Then let's make it so.
Congress has the right to conduct investigations of issues under its purview, and right now, it has the right to look into health care issues. The feds fund billions of dollars worth of health care every year, and there is no doubt that it can look into the issue of right to die issues as they impact federal health care policy. (leave aside the issue of whether the federal government should be involved with health care, the fact is they are).
Congress wants to investigate the Schiavo situation, the same way it investigated the baseball steroids issue by calling the players in to question them. This is an individual case, but it may have some implications on health care policy in general, and the fact that a state can allow a person to starve to death in this case without adequately providing for protection of her rights is something that the Congress wants to look into. So, not only does it want to examine the procedural aspects of the right to die in Florida, it may want to examine the facts of the case, to determine if an "innocent" woman can be put to death by a seemingly benign system.
So, the Congress lawfully subpoenas witnesses to a hearing, including the woman whose life is at stake. The woman, Terri, cannot testify, obviously, but her condition can. The Congress can order tests of her, and make its own determination as to her present condition, which will then be helpful to Congress in deciding what it thinks about the protections afforded by state law.
There is a federal statute that provides that tampering with or obstructing a Congressional witness, or harming evidence before a Congressional inquiry, is a felony. Allowing Terri to die would violate this statute.
The President and Congress are allowed to invoke the assistance of the US Marshalls service to protect witnesses in a congressional hearing. If not the Marshalls, there is a federal agency that delivers subpoenas and transports witnesses that would be the proper one.
The President, to uphold federal law, can therefore order the marshalls to enforce the Congressional subpoena, deliver Terri to Congress' custody and protect her life. This will include reinserting a feeding tube so she will be alive and available for Congress' investigation.
Granted, this is only one scenario. President Bush is probably examining many options. But I hope you would agree that your statement that "there is no basis in the Constitution for President's Authority to do this" is just flat wrong.
See the Preamble, which declares the purpose for which the Constitution was written.
Intrinsically evil laws or judicial rulings are null and void.