The polls are clear that the public as a whole is blaming Trump, and rightly, but of course it's also true that Pelosi and the Dems could end this crisis and help the affected people at any time they chose, by giving up something that's pretty insignificant in reality, however big a political symbol it may have become. They are prioritizing their political victory over those people's livelihoods, just like Trump is doing. And of course just like the British government is doing in their own crisis.
Not really sure how this is going to end, but it might take quite a while before we get to that end.
I suspect another reason the Dems aren't compromising is that this is a fairly unique situation where it's the President causing the shutdown. If you give Trump a 5 billion plus wall because he's holding federal workers hostsge, what's he going to ask for next time?
I suspect negotiations would have been underway but for Trump explicitly stating, on TV, that he'd happily take credit for the shutdown. After that, and given that this was the very first piece of legislation post their election, the Dems have no real way to say yes.
Had Trump been cleverer about this, he could have gotten his initial 1.3 billion dollar ask in exchange for the protection for Dreamers he's now offering. It's a ridiculous ask, but it might have worked. Now, I don't know. I think both sides see the humiliating defeat of the other as the only possible way to "win". That's not a standoff with a quick resolution.