There's a reason for using distilled or other purified water in such designs. Hopefully they'll get it cooled down before it becomes a serious problem of its own.
But I don't know anything quantitative to say whether the buildup will limit them in days, weeks, or months. Those reactor cores stay hot for a damn long time.
Yeah...I don’t know if you could read the article or not. But they estimate 99,000 pounds of salt has accumulated in just one of the reactors. I mean...WOW!