Lyric discussion by DavidGrimmer 

Cover art for Don't Let's Start lyrics by They Might Be Giants

The phrase "don't let's start" basically is a fatigued expression asking that you and I not once again start up the same argument. The guy is telling the girl "let's not get into this, because it will start a huge fight".

The "D world destruction" bridge is a play on the old 50's and 60's bit of spelling out words in love songs (like "L is for the way you look at me" in "L-O-V-E" by Nat King Cole). One of my favorite things about TMBG is how they recycle bits of pop culture and turn them to their own twisted designs.

Deputy Dog was a cartoon character (from Hannah Barbara, if memory serves me right). I'm pretty sure they are just using it as a nonesense scat because it's fun to say really fast.

Deputy Dawg was a very pessimistic-sounding animal with a perpetually hang-dog (snicker) expression. So using Deputy Dawg in the scat reinforces the resigned, fatalistic attitude of the song.