I read an oped piece by Ted Cruz over on Politico saying something very similar - that both on PP and on Iran, a sizable majority of the American public supports his hard line.
But the actual numbers I'm seeing, like the recent YouGov poll, show that America is pretty evenly split on both topics. As far s I can see there is no clear majority, much less 70%, in favour of Cruz's stance on either topic.
What's clear is that Republicans overwhelmingly support Cruz on both points, but that's a very different thing.