Antisemitism, as I've mentioned in a couple of other comments in this sub, was pervasive throughout the Western world through the first half of the 20th century. It's easy to point at Nazi Germany as the only ones that had anything against the Jews (and they certainly carried out a tremendous atrocity against them), but anti-Jewish sentiment was very much present in the US as well as Europe. Americans would not have wanted to take on the burden of a large influx of an "undesirable" population, especially before photos of their systematic genocide were plastered on every US newspaper. The fact that the effects of the Depression were still very much around would have only served to reinforce this apathy towards the plight of the Jews.
The US also had a pretty firm desire to remain isolated from another European war, so denying entry to these immigrants was partly an attempt to keep out of it.
It's also possible that 200,000 denied visas were just a side-effect of bureaucracy, but I'm not well-enough versed on US immigration policy of the era to talk about that.
EDIT: Sources!
A Time for Healing, Edward Shapiro; middle of pg 3 is a good place to start and it talks about antisemitism in the US before, during, and after WWII, but the whole book (and series of books, even) is really worth a read
Eagleton Institute of Politics website that states "between 71% and 85% of the U.S. public opposed raising the refugee quota" in 1938, despite awareness of Jewish persecution in Germany; this page also talks a bit about American isolationism's relationship with immigration attitudes
An article from the US Holocaust Memorial Museum website about the US and European Jews; this provides a little bit more context for the embedded antisemitism that wasn't as explicit as we tend to think it must've been
/u/vhcngh, are these good sources? I am not a professional historian, but a passionate enthusiast. If they are satisfactory, I will strive to provide these kinds of sources in this format in future responses I give on this sub.
After Hitler rose to power in the 1930s, the United States still had very restrictive immigration laws that were made during the 1920s, so legally the country couldn't take many refugees without a change in the law. Changing the law couldn't happen because the Great Depression had made jobs scarce and immigrants meant more competition for jobs. We also did not know the full extend of the Jews plight. Our intelligence knew that the regime was severely reducing their civil liberties, but we did not know the full extent of what was happening in the camps. Antisemitism was not a big reason Americans didn't take in more refugees, and there were even civilian organizations, some organized by Jews, but others by Christians, that helped Jews get into the US or, at least, out of Germany.