What "better deal"? The Paris climate agreement is entirely voluntary; each country determines its own contribution to reducing global warming and there is no enforcement mechanism. It's aspirational and America gains nothing by pulling out of it.
We know that generally the majority people support some action in flavor of climate. So any question that is phrases in that light will reflect that and have almost nothing to do with Paris specifically.
> It's aspirational and America gains nothing by pulling out of it.
Who cares about America? How is that relevant to politicians? Some climat change that might happen at some point in the future when they will not be in office anymore. What even is America? The people now living in America? The future people in America that don't vote? The country itself?
Non binding international agreements are about signalling and internal politics.
If Trump actually believed that 70% of the people would vote against him if he pulled out of Paris he would never have done it, but that is not relevant because they want, so he doesn't care.
Trump's decision (assuming it's a rational one and not fed by ignorance) is signaling the reverse: he's telling his supporters that climate change is a myth. And this is why he's getting pushback from other countries.
With these sort of one dimensional political questions its mostly about how you ask.
If it had said "Do you support the presidents effort to renegotiate the Paris treaty to get a better deal for the US?" you would have gotten 70% in the other direction.
Most of these sort of 'studies' are just marketing.