The timing is also incredibly sudden. Graduate students have been in the US for 5-10 years. They have leases and cars and friends. Giving them a few weeks before deporting them is cruel.
Note: I support the lawsuit, I have many friends who are or were international students, I live in Boston, just wondering how this would affect research-based grad students.
I do know that I have faculty friends who have had their grad students come to them in tremendous distress related to this policy. So at least some people believe that this would deport graduate students who have advanced to candidacy.
[1] https://educationusa.state.gov/your-5-steps-us-study/apply-y...
[2] https://ois.usc.edu/students/maintainingstudentstatus/, https://international.northeastern.edu/ogs/maintaining-statu..., etc. (many schools have some version of this FAQ page on their websites)
This is the intention of the Trump admin's policy: discouraging people from immigrating by whatever ugly means necessary, no matter if illegal or not. This has been a consistent line from the beginning with the infamous "muslim ban".