What would you do? #124 - Facing river shove / raise

Sorry; this is somewhat of a weak WWYD, but it's at least a little interesting...

Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

BTN: $50.00 - 26 / 11 / 50% steal / 0% 3bet @ 19 hands
SB: $51.70
BB: $43.70
UTG: $52.25
UTG+1: $98.35
UTG+2: $77.75
Hero (MP1): $54.30
MP2: $53.15
CO: $50.00

Pre Flop: ($0.75) Hero is MP1 with 6h 8h
3 folds, Hero raises to $1.75, 2 folds, BTN calls $1.75, 2 folds

Flop: ($4.25) 5c Qs 6c (2 players)
Hero bets $2.75, BTN calls $2.75
Semi-bluff; middle pair and backdoor straight draw.  Not too happy with the call.

Turn: ($9.75) 4d (2 players)
Hero bets $6.75, BTN calls $6.75
In retrospect, I'm really not comfortable with this bet.  I want to push him off of the hand, but I don't think I'm representing anything credible here.  Just an odd spot.

River: ($23.25) 7h (2 players)
Hero bets $18, BTN raises to $38.75 all in, Hero calls $20.75
But I'm bailed out by the river.  This is a clear call, right?  Anyone laying down a $20 raise here?

Final Pot: $100.75
BTN shows 3d 3h (a straight, Seven high) - He had the same nasty intentions as I; he held on til he rivered his backdoor straight.  He didn't expect me to show up with an 8 though, from an MP raise...
Hero shows 6h 8h (a straight, Eight high)
Hero wins $97.75
(Rake: $3.00)