Dear math-challenged announcers, and you know who you are (Mr. Manaman),
When a team is down late in regulation or overtime, generally speaking, yes, they do need threes. Example: you're down 4 with 20 seconds left. If you hit a 2 right away, and you steal the inbounds pass and hit another 2, then no, you didn't need a 3. In any other situation, though, yes, you did. (It's also possible to foul, watch them miss two, and then come down and hit a two, but about as likely.)
What is much, much, much more likely is that your opponent is going to score again. Anything less than 10 seconds a possession is luck. You should expect your opponents to hit free throws, not hope that you'll somehow hypnotize the ball out of their hands. If they get two free throws per possession, you need three points per possession.
Learn to count.