Yes, she projects a lot.

Straight from NYC government: nyc.gov - Asylum seeker update

The problem is a real thing, just not as portrayed in the shouty right-wing birdcage liners: pbs.org - Migrants face eviction from emergency shelters in new york city as holidays approach

nytimes.com - NYC migrant crisis explained

Since this is a pay-site, I'll excerpt:
“While New York City will continue to lead, it’s time the state and federal government step up,” Mr. Adams said at a recent news conference.

As the city struggles to respond, Mr. Adams has also begun to discourage migrants from seeking refuge in New York City. In early October, he traveled to Mexico, Ecuador and Colombia to meet with migrants and spread the message that New York City “has reached capacity.”

And what Adams has been saying (back in April):
nytimes.com - Adams biden migrants
As New York City was inundated with asylum seekers bused from the border last year, Mayor Eric Adams cast blame on the Republican governors of Texas, Arizona and Florida.

But when the cost to feed and house the migrants quickly escalated, Mr. Adams shifted his ire to the federal government, pressing for more emergency aid, and to allow asylum seekers to work legally.

And, yes, he did single out Biden (last spring), and continues to do so. Which is mostly in error, because Biden doesn't control the purse strings. Congress does. I think he could pull a few levers (like FEMA), but that would probably be a misuse of those funds. NY state is considering allocating funds to the city (though hasn't done so yet, I don't believe).

And now Mayor Adams is under scrutiny for possible campaign shenanigans. Apparently it isn't the first time Adams has endured probes into his activities, even when he and Biden were buddies.

politico.com - Adams biden NYC (rated left-center, highly factual)