No country has an obligation to take in migrants in general.

True refugees make up a minority of the people we're talking about. It's been that way in the past, and it's true now even though the numbers are much bigger. I read a good article a few months ago behind the logistics and economics of human trafficking. I forgot most of the details, but it listed several reasons why an increase in legitimate refugees (i.e. Syrians and Eritreans) also leads to an increase of people who migrate for purely economic reasons. People who have understandable reasons for trying (if you lived in a third world country, wouldn't you like to move to Germany or the UK?) but who have no reasonable claim for asylum.

Multiple ideas have been put forward in which Turkey would put more effort in preventing human trafficking across the sea and, in return, European countries would take in a fixed number of genuine refugees every year, until the Syrian conflict has ended. Turkey would also receive some financial compensation for this scheme. This would be great if it could be made to work but...it's Turkey we're talking about.

As for frau Merkel: I also think that the particular speech she's been criticized so much for was ill-conceived, but mostly because of the predictable political backlash. I don't buy the assertion that one speech will suddenly cause millions of people to pack their bags. There was a huge spike of migrants shortly afterwards, but most of those people would have been on the move for weeks before that. On the other hand, David Cameron isn't known for lofty welcome speeches but people are still trying to cross the canal tunnel in droves. What does that tell you?