While I haven't read Goldhagen or scholars with a similar viewpoint directly, I frequently encounter the following argument that seems very Goldhagenite to me: "The Germans tried to murder Jews up until the end of the war, the trains went to the death camps even when the war was already being lost and more resources were needed for the war effort, this clearly shows the German eliminationist antisemitism."
Eliminationist Antisemitism was defined by Goldhagen in Hitler's Willing Executioners. One key feature would be that the germans were "of one mind with Hitler" in terms of antisemitism. This would explain the continuation of the murders late into the war. Now, among other criticisms, Browning pointed out that the same willing executioners were as willing to kill handicapped or Russian POW before the mass murder of the European Jews began; also he got the diverse ways in which German society was antisemitic wrong.
So to me, eliminationist antisemitism is not plausible - but what other explanations are there? Since Goldhagen's views are not widely shared, I assume other historians tried to answer this question - why continue the killings until the brink of defeat. Those would be the answers I'm looking for.
p.s. In no way do I want to deny that ordinary Germans were willing executioners, or that there's antisemitism entrenched in German society. But I think the actual history is more complicated than made out in the model of eliminationist antisemitism.
EDIT by F.G.: For background on functionalist/intetionalist see here.