He'd be ripped apart because of his wife as well. Every policy she supported in Denmark, such as relaxing anti immigration rules, working with the furthest left party (Green) in coalition, increasing tax revenue through offering tax cuts to the highest earners, along with the investigation into his tax status that was concluded with no fraud found, would be used as proof that he was the herald of a plot to flood the country with immigrants, make billions from tax frauds, etc, etc.
I daresay they'd try to find some sort of racism/antisemitism somewhere as well, claim that he was a secret Militant Labourite, loads about his parents, have photos of him at dos with his wife where she met people who were rich and powerful, etc, etc.
Mind you, if the original JC reappeared and wanted to become Labour leader, he'd be painted as this dodgy immigrant from a teenaged single mother wanting to steal the food from the mouths of the children of the temple traders (and next, he's coming for YOURS), showing communist tendencies by feeding so many people, causing wholesale ecological disaster by pillaging the fish from the Sea, putting hardworking fishermen out of business, causing crops to fail by stopping rain so he could perform his magic trick of standing on the water and, worst of all, posing a threat to the functioning of the NHS by performing healing free of charge. Oh, and despite being UNMARRIED and HANGING OUT WITH FISHERMEN, also being seen with his Very Close Friend Mary Magdalene who has been rumoured to have a dubious source of income, associating with the known anarchist that is his cousin John and threatening to steal YOUR WEEKEND by saying it's OK to work on the Sabbath by picking a few grains to eat.
He'd also clearly be portrayed as an Antisemite.