You would not need nuclear weapons in space.
A steel rod dropped from space and that could be guided to a target would do a lot of damage upon impact (without any radiation).
I am not sure if weaponizing space is a good thing or not, nor am I sure the Russians (or Chinese) have not already done so. Perhaps the President has received a briefing where he has been told that both Russian and China already have weapons in space. Which would help explain his action.
I believe we used Rods from God to take out North Korea’s underground nuclear test site killing all those scientists of theirs. That’s why they decided to come meet us at the bargaining table.
Wikipedia says "China's anti-satellite (ASAT) program has been under development since 1964." Russia has done the same for the same amount of time. It's long past time to acknowledge this openly and create a MAD capability.