It wouldn't take that much trimming. The Warriors gave up two firsts and two seconds to get rid of the contracts of Biedrins, Jefferson, and Rush. That was a combined $24 million over one year.
If the Celtics make no mid-season deals, Ainge should be able to salary-dump Bass and Lee (a combined $18 million over two seasons) for no more than a first-round pick each, clearing enough cap space to sign a player with 0-6 years of NBA experience to a max contract (or coming pretty close). That would effectively be trading Bass, Lee, and two firsts for a big contract guy.