No I'm fairly certain no politicians in the United States are calling for bans on euthanasia.
As the question mentions, right wing politicians do support a ban on euthanasia for people. A major reason for this comes from catholic social teaching that life should begin at conception and continue until natural death. This comes from the idea that: (from a Vatican published document)
Human life is the basis of all goods, and is the necessary source and
condition of every human activity and of all society. Most people
regard life as something sacred and hold that no one may dispose of it
at will, but believers see in life something greater, namely, a gift
of God's love, which they are called upon to preserve and make
Life is a gift of God, and on the other hand death is unavoidable; it
is necessary, therefore, that we, without in any way hastening the
hour of death, should be able to accept it with full responsibility
Meanwhile when the Catechism of the Catholic Church talks about animals, it says
2417 God entrusted animals to the stewardship of those whom he created
in his own image. Hence it is legitimate to use animals for food and
clothing. They may be domesticated to help man in his work and
leisure. Medical and scientific experimentation on animals is a
morally acceptable practice if it remains within reasonable limits and
contributes to caring for or saving human lives.
2418 It is contrary to human dignity to cause animals to suffer or die
needlessly. It is likewise unworthy to spend money on them that should
as a priority go to the relief of human misery. One can love animals;
one should not direct to them the affection due only to persons.
So Catholics believe in being stewards of animals, but not elevating to the level of humans and treating their lives with the reverence due to human life. This distinction is fairly common on the American right. I think a telling statistic is from a survey that found "ten percent of liberals indicated they are vegetarians, compared with 3 percent of conservatives."
While it is difficult to prove a negative, I believe that this helps explain why some American political groups would support a ban on euthanasia for humans but none would support a ban on euthanasia for animals.