Unless there is overwhelming support for this via polling or huge Senate gains...it will backfire and invite further retaliation.
The response should not be "we need to change the rules," but rather "we need to find a way to be more popular, win more elections, convince more people of our policies."
I actually think Biden has the right idea, measured and patient. Try to strike a bipartisan agreement on certain reforms. Term limits might be some low hanging fruit to go after. But just expanding the court because you can...would probably end them as a party for the foreseeable future.