Long term, however, that might prove to be a failing strategy.

We already know:

1. American citizens have already been deported by this administration.

2. The USSC has given a powerful incentive to this administration by claiming, in a shadow docket ruling, that the US has no responsibility for the welfare of people deported to foreign gulags (note: this is exactly why Germany began constructing so many of its death camps outside the geographic borders of Germany).

Neither of these things are strictly correct.

The administration has not deported adult citizens. The administration has deported minor children that are citizens with their parents, but it is not clear whether (and it's pretty unlikely that) they took the position that the children were legally subject to deportation or whether they were preserving family units at the request and with the acquiescence of the parents. There have been a bare handful of instances over the years where U.S. citizens have been deported by mistake under this and prior administrations, but I do not believe the administration or the courts have ever claimed they had a lawful basis for deporting them.

As for the recent shadow docket ruling, the SCOTUS did not reach the merits. They simply stayed the injunction. The media has a very, very bad habit of reporting procedural rulings as if they were decisions on the actual arguments of the case - so that if the SCOTUS reverses an injunction stopping people from being deported to third countries it gets reported as if the SCOTUS has determined that the U.S. has the power to deport people to third countries. Even though those are two very different things.