Earlier quoted context omitted.
As I understand it, even though the "informal proposal" is about "prioritising local workers over foreign ones" the actual proposal only requires informing the regional unemployment offices of open jobs, which might(?) not violate freedom of movement.
The issue is the following: In February 2014, the Swiss voted in a referendum to introduce quotas for all migrants in Switzerland. The referendum, which requires Switzerland to have annual quotas for immigrants, does not take effect immediately but requires the Swiss government to implement a quota system within three years. Nothing to do with regional unemployment offices.
https://www.parlament.ch/en/services/news/Pages/sda-spk-n-20...