The poll is by Tamedia, a reliable polling company (as much as any polling company can be). It has been widely cited in others media, including the public one.

There is significant support for the initiative. Initiatives tend to lose steam as time go by, so it might not be enough in the end, but like Brexit, don't underestimate it.

Let's not pretend like Tamedia doesn't have a bias that has a significant overlap with people who tend to follow the SVP vote suggestions. Much like it's well known NZZ will come out with articles against the 10 million cap because it has a significant FDP bias. Swiss private media has well known biases and is just thinly veiled propaganda most of the time.

But SRG does a good job at presenting things neutrally.

Of course nobody should underestimate the initiative. But I think you will agree that "Most Swiss back initiative to cap population at 10 million" is a sensationalist title since most people probably didn't make up their mind about their vote yet.