It's barely a blip on the nation's demographic radar -- 11 percent of U.S. births in 2004 were to women who already had three children, up from 10 percent in 1995. But there seems to be a growing openness to having more than two children, in some case more than four.
source
I sense there is a larger openness, but I don't think it's very extensive. I think it has to do with increased religiosity and exposure on the internet. When I post on Catholic Mom message boards, I regularly find moms of four or more children. It's not that they're numerous in real life, but they tend to congregate on Catholic Mom boards. And that exposure makes large families seem less unusual. Myself, I grew up with three siblings, and I often thought about having many kids. I am not closed to having many children, but there are practical factors that make it difficult to make it a reality. For me, it's not the lack of money, it's the lack of network-- the lack of relatives who can help out. My oldest is autistic, and while I do get government assistance, I do have to go through the bother of finding qualified help.
I note that this article doesn't have a lot backing up its claims, but I sense this is true, at least in the Catholic boards I have frequented.
Check out the Big Blue Wave Message Board