If you had written that you had KJ against KQ I could have felt sympathy for you. K3 was a really marginal hand to call him down with, even with the K on the river. Ted Forrest pushed all-in pf 3 times yesterday with K7 & once with K9 on Poker After Dark v.s. Paul Wasika (h/up challenge). Some guys love to take a bare K all the way to the river.
Basically, when he's aggro, blinds are high, and your a 3:1 underdog in chips, consider folding pre-flop or going all in. If you still have 10bb you might get him to fold Qx. If you're a passive player that can make your strategy easier. Fold everything marginal, go all-in with KJ or better.
If you get no cards at all, then go/call all-in with at least 6bb (no matter what) so that if you do manage to double up you win enough chips to hurt him the next hand you find. If you wait until 3bb or 4 bb before you pull the trigger you'll still be on life support even if you do win the hand.