Taking a longer term view, the US has fallen from around 4% of global births in the 1950's to 3% by 2000 to around 2.6% today. It's share of global population has come down from around 6% in 1950-1960 to 4.3% today and will continue to decline. The US over the coming decades will increasingly resemble much of the rest of the developed world, low fertility, an ageing and old population and a shrinking one.
In terms of what impact migration can have on fertility, one issue is the main source of migrants for America today is Asia and Asian American fertility looks like it fell to around 1.5 last year, when most migrants were from Central & South america they raised overall fertility, today migrants from Asia lower overall fertility, migration will not solve the issue of declining fertility, it may exacerbate it.
Yes and no on immigration exacerbating declining fertility. I would like to see some data on whether Chinese, Korean, etc. immigrants actually have fewer kids than "native" Americans - I suspect that they have more. Migration from one country to another itself is something ordinarily undertaken by a certain type of person with characteristics that tend towards higher birthrates.
Also, a large and growing portion of the immigrants to the U.S. from Asia are from countries with relatively high birthrates, like India, the Philippines and Vietnam. It's not like most Asian immigrants to the U.S. are from Japan.
