Well, while not all Dems are supporting this, and incidentally not all on the right are defending terri's right to life, those on the Left not doing so mainly fall alone a few reasons.
Perception the Judiciary's authority is being challenged. This is true, and for the Dems, terrifying.
Also, grassroot supporters are firm believers in euthanasia and abortion. This is seen as being a threat to their viability.
Those on the right, on the other hand, keep citing privacy, limited government, and state rights. Oh, and both sides argue no one would want to live like that.
Many "Republicans" who want Terri dead fail to cite the real reason: they know she's not PVS and are afraid that if she lives their profitable death mills will be exposed.
Taking your arguments point by point:
Fight perception that judiciary authority is being challenged, but not at the expense of a helpless woman.
This is not euthanasia, because outside of her husband's biased verbal testimony there is no other evidence she wants to die. Besides, most neurologists claim she feels no pain.
The highest ideal as a conservative must be the value of human life. It supersedes all other conservative values, except for killing an enemy of the state,of course.