paying for that push poll.

PUTIN

When a campaign commissions a poll to get information that the campaign intends to use, that's partisan, but it's not a push poll. If I were running one of the Republican campaigns, I'd want to know the answers to the questions you were asked.

A push poll is one that's not intended to get information, but to disseminate a point of view, using the guise of a poll so as to gain credibility. An example would be, "Would you be less likely to vote for Sherrod Brown if you knew that he ____ {insert absurd falsehood about Brown}?"

to indicate agreement to their set answers.
It was not conducted by a live person, but a recorded questioner.
It purported to be a "public opinion poll".
I considered the first few questions were to put me at ease with the poll.
There was no alternative to what was (for me at least) the final question - For whom would I vote in the Republican primary?

The example you cite is certainly a type of push poll, but not the only one.
Whoever commissioned the poll or whoever wrote the wording was looking for certain responses, not conducting an honest survey of public opinion. That qualifies as a push poll.

There will evidently be a contested Republican primary for the right to run against Brown. For any Republican contender, the first hurdle is winning the primary. If a poll responder likes Brown and has no intention of voting in the Republican primary, then the pollster wants you to hang up at that point. Nothing you might say will give a GOP candidate any information that's useful to his or her immediate concern.

At least, that's how I'd interpret their motives.