The last time she tried getting the help of another great house she ended up married to Tyrion. Not surprising that she would not want to put herself out there again.
Referring to the Tyrell or Lannisters? I mean, Sansa told Dontos about the wedding proposal of the Tyrell, who passed it on to Littlefinger, who informed Cersei/Tywin (if I remember correctly). So really, she once again mucked that up herself but I don't really remember if she understands the position both houses take because at that time she didn't know Dontos was Littlefinger's man. By the time she's in the Vale, she does know this but I don't think she realizes she basically has Littlefinger to thank for the marriage to Tyrion.
While rereading Littlefinger's plotting in the Vale, it just struck me as odd Sansa wouldn't be more assertive. Arya now and then displays quite some knowledge of the historical bonds between the houses, Sansa - supposedly more ladylike - sure as hell knows of the Stark/Arryn history. The Vale joined Roberts rebellion early on while the Lannisters had a wait and see approach and Tyrell stayed loyal to Targaryen. So yes, shit went FUBAR for her trusting the Lannisters and falling for the charming Tyrells was just as naive, but here's a house with 'As High As Honor', connected to both Stark and Tully, and stayed neutral up till now. Sansa has some chapters in Winds of Winter, right? Quite curious to see if she sticks to Littlefinger's play or branches out to play her own.