They need to create this hysteria around it, because they are hoping that other nations will be so horrified that it will be top of their agenda.
As has been pointed out many times, this is such a silly argument that anyone using it has to be arguing in bad faith.
The problem is that there is a huge assymetry between the numbers of UK nationals in, say, Spain and the number of Spanish people in the UK. You can't persuade the Spanish government by threatening to send Polish citizens home. In the same way, the Polish government has a lot to lose, but very little to offer in return, because few Britons live in Poland.
The only country where there is anything like symmetry of numbers is France; but even there, the argument doesn't really hold, because the vast majority of French people in the UK are young people in salaried work, whereas many if not most Brits in France are retired or "self-employed" and living off top-up benefits. I would put the proportion of Britons in France in salaried work at fewer than 10% of the total, and that's probably generous (it wouldn't surprise me if the true figure were below 5%).
People on these threads often don't have a clue how brexit is presented in the European press, because they don't even have enough French/ german /spanish to read a simple newspaper article. The truth is that there is zero hysteria and, for the most part, this issue is of no interest whatsoever to ordinary French and Spanish voters. This means there is very little for politicians to get excited about.
I see no evidence of any appetite at all for kicking Britons out, except perhaps in the far right fringe - though efforts will undoubtedly be made to restrict British access to benefits and healthcare, and this will result in people leaving of their own accord.