It does once you get to the 4,001st page of the results (which is actually 100k items): "Sorry! We can't process this request. This request exceeds the maximum search results depth." The error page even includes a link to "LC for Robots" (https://labs.loc.gov/lc-for-robots/), a list of APIs, since few humans are going get that far on their own.

The number here also seems less misleading because all 324,782 results do seem to exist. It doesn't want to generate a pagination for the entire set, but you could get to them by choosing different formats, date ranges, collections etc. The number Google repors, as far as I can tell, needs to be taken on faith.

Ahh, looks like the limit on results is 100,000 items on that page. https://www.loc.gov/search/?q=god&sp=4000

But you can subdivide the search results by date and get every item on your original list: https://www.loc.gov/search/?dates=1890/1899&q=god&sp=1808

So, they have and can show you every single one of those 324,782.