The biggest embarrassment for deniers is the inability to provide a compelling explanation for how millions of Jewish vanished in the Nazi camp system (at least 3.3 million Jews were deported to camps, and only at most 300,000 were found alive in the camps at the end of the war, so you have 3,000,000 Jews disappearing in Nazi custody).
The resettlement thesis propounded by most deniers, as a way of escaping the disappeared Jews problem, is self humiliating.
If a settlement of millions of Jews (a country, really, with a population greater than contemporary Estonia) existed in the 1940s we would have some evidence of it. Yet there is no trace of physical infrastructure (ruins of homes, apartment buildings, stores, etc) communications (radio transmissions, letters home from resettled Jews to mommy), documentary evidence (e.g. German documents referring to this nation of millions of resettled Jews), economic activity, or testimony corroborating the existence of this Jewish atlantis the deniers claim existed.
Another problem for the resettlement thesis is that the Nazis never occupied Asian Russia (the North Caucasus are in Eastern Europe), and would have never resettled Jews in Europe. This would have contradicted their longstanding policy of removing the Jews from Europe.