Is it illegal for Congress to change the number of justices on the Supreme Court?
No, but it would need votes in the both the Senate and House. The important thing to consider is the following:
"As with other Democratic efforts to undermine established rules of order, any attempt by the Left to pack the courts could set a dangerous precedent and eventually backfire against them."
Technically speaking, you need a 60% vote to enact this change. However, if the majority party decided to take away the filibuster rule on this occasion, you can get it passed with a simple majority. So, assuming that a Dem wins next term and the Senate flips with the house remaining the same, this could happen. But it then opens the possibility of the Republicans doing the same when they are in power. Considering the pandora's box the Dems in the Senate opened with the same rule change they enacted during Obama, and how that lead us to having two new Trump appointees on the court, I would not consider the move prudent. I can't see it ending well in the long run and would only make the court more political.
Do we really want to make the courts more political with this?
The only time that I know of the court being packed was during the Civil War, and one could make a pretty compelling argument that this was to combat the objectively bad practice of slavery. To pack the court for other less serious issues would be dubious. FDR tried to do the same during his presidency and it backfired on him.
Additionally, I cant see this happening anyway. It really appears that it is only those low in the poles that are calling for this, more then likely a way to score percentage points and stay alive.
