[knarf]

"Actually, it isn't contradictory. I had to read it closely to understand, but the use of the word "if" is what makes it make sense. While 65 percent say she should serve a full term if she runs for re-election to the Senate, 61 percent say she should run for the White House. The use of the word "also" adds to the confusion, but where the word is placed means that respondents aren't saying she should do both."

Why do I get the feeling the respondants haven't a clue about what you just parsed?

(In my best Baby Huey voice ... )

Question #1 .... duuuhhhhya!

Question #2 .... duuuhhhhhya!

[drjimmy]

Why do I get the feeling the respondants haven't a clue about what you just parsed?

The problem isn't with the survey, it's with the story about the survey. It combines answers to what must have been two separate questions into one sentence. The questions would be something like:
Should Hillary Clinton run for the White house instead of running for re-election to the Senate?
If Hillary Clinton does run for re-election to the Senate and win, should she serve a full term and not run for the White House?
People can answer "yes" to both of those questions without it being contradictory.