TT on a 678 flop and lots of action

[SlantNGo]

First orbit at the table, no reads on either opponents. On the flop, I didn't think a 3-bet would accomplish much in late position so I decided to wait for the turn card and raise a blank. Little did I know, it came back to me 3-bet and capped. I called here with the gutshot draw, and again for the first turn bet. 2-back to me and I no longer had odds to draw to the gutshot. My question is, should I have been out of this hand much earlier?

Party Poker 0.50/1 Hold'em (10 handed)

Preflop: Hero is CO with T/images/graemlins/diamond.gif, T/images/graemlins/club.gif.
UTG folds, UTG+1 calls, UTG+2 calls, MP1 folds, MP2 calls, MP3 calls, <font color="CC3333">Hero raises</font>, Button folds, SB calls, BB calls, UTG+1 calls, UTG+2 calls, MP2 calls, MP3 calls.

Flop: (14 SB) 6/images/graemlins/diamond.gif, 7/images/graemlins/heart.gif, 8/images/graemlins/heart.gif <font color="blue">(7 players)</font>
<font color="CC3333">SB bets</font>, BB folds, UTG+1 calls, <font color="CC3333">UTG+2 raises</font>, MP2 folds, MP3 calls, Hero calls, <font color="CC3333">SB 3-bets</font>, UTG+1 folds, <font color="CC3333">UTG+2 caps</font>, MP3 calls, Hero calls, SB calls.

Turn: (15.50 BB) 3/images/graemlins/club.gif <font color="blue">(4 players)</font>
SB checks, <font color="CC3333">UTG+2 bets</font>, MP3 calls, Hero calls, <font color="CC3333">SB raises</font>, <font color="CC3333">UTG+2 3-bets</font>, MP3 folds, Hero folds, <font color="CC3333">SB caps</font>, UTG+2 calls.

River: (25.50 BB) 7/images/graemlins/club.gif <font color="blue">(2 players)</font>
<font color="CC3333">SB bets</font>, UTG+2 calls.

Final Pot: 27.50 BB

[Bez]

The hand turned out ugly but I think you played it correctly.