Jon is king in the north ,when he finds out he's a targ and pine for the iron throne...

[Danny-]

...Will the northern lords and the starks back him or still demand independence? 

I think the northeners will get pissed when they find out he bent the knee and when they find out he's aegon targarean it will add fuel to the fire.

[King Jon Snow Stark]

He's still a member of House Stark. He was raised in the north. He would be the most sympathetic king when it came to the north. But he gave all rights to the iron throne when he bent the knee. The north might have back him if he wanted the throne. 

I can see some northerners (like Sansa) being pissed at him for giving up the northern crown and not wanting the iron throne. 

[Hoo]

Jon will find out from Bran or Sam.  The bending of the knee will be null and void.   Then, he'll probably recommend Sansa to be the Queen or Warden of the North at one of the councils.  I doubt he will be faced with another choice of lying for the sake of truce, this time to his bannermen, to Dany.   Maybe Sansa will ask him to lie, hehe. Then, Sansa will have to decide whether to bend the knee or not.  If Sansa does not bend the knee, Jon's choice will be interesting.  Where will he get the army to do what he wants to do, to do what he promised to Dany?

[jcmontea]

Jon will not back out of his bending the knee to Dany i think. An oath is an oath. He did not bend the knee because of her superior claim. He bent the knee because of who she is as a person. 

As Jon says, the northern lords will back Dany once they see who she is. Besides, what is there alternative. Are they going to risk fighting the white walkers on their own because they don't want to support Dany? That is suicide. Then after the White Walkers are defeated. Would they really not back her after she literally saves the North? Unlikely. They will be on their knees calling her Mother. 

The truth is there is no time for a northern unrest plotline. The White Walkers are already past the wall and Bran knows it. Once Bran spreads the news they will have no choice but to accept Dany.

[TyrionFan82]

 I agree, the North will bend the knee. Dany's going to help defeat the NK and Co. and who'd Stark bannermen go with? Cersei? C'mon! They'd be signing up like gangbusters. Now the sticking point is SANSA. Despite the fact she'd be Warden of the North the revelations about Jon and his bending the knee might or will disturb her.