My understanding is that the U.S. birth rate is near or below replacement rate, but I don't understand why. If more people are being born than are dying, won't the population continue to grow?
When you hear that "the U.S. birth rate is near or below replacement rate", what is probably meant is that the total fertility rate (TFR) is below 2.1 (replacement rate).
It is possible that the TFR is below 2.1, while births exceed deaths. One way this can happen is if there's a rising share of women entering reproductive age.
This is actually a fairly common phenomenon: Many countries have had TFR below 2.1 for many years but their populations have continued to grow. For example, China has had TFR below 2.1 since 1992 but births have continued to exceed deaths every year.
This answers your question. Apparently the replacement rate for the population of the US is when the average birth rate of specificly aged women is at 2.1 babies per woman. Annual deaths and births are probably not a bad indication of population growth, but when it comes to this specific measure (the replacement rate), they are irrelevant.
I just have to say, I personally wouldn't post such a question on an Economics SE. Perhaps it's best that you move it to the Statistics SE.