Both stories were uncomfortable for the Government. Both are also great examples of the need for a sophisticated understanding of the drivers of public opinion.
Ipsos Mori data shows anti-EU sentiment is at its highest since the early 1980s, and a clear majority would support a referendum. So the Commons rebellion was with the grain of public opinion.
In the long-run though, David Cameron is right to calculate that it is more important to deal with the economy first.
Only four per cent tell us Europe is among the most important issues facing Britain, well behind the economy at 68 per cent.
While Europe is important to some, the arguments are often fundamental ones about Britain's national identity rather than financial ups and downs. We know, though, that economic competence was the most important issue at the last election. The potential political dangers are also well known. Since moving into government, public opinion has switched from viewing the Conservatives as a united party to a divided one.
Nor are the answers to public attitudes on immigration straightforward. A clear majority supports the coalition's target of reducing net migration. However, to do this the public is less likely to be thinking of students (one of the largest immigrant groups) and more likely to think of asylum seekers (one of the smaller groups).
Similarly, the group the public would most like to see reduced (low-skilled workers) is an area where there are significant policy constraints from the EU, over which the Government has little control. This mismatch creates a challenge for the Government in being seen to fulfil its promise.
These are two issues where public opinion at first seems clear-cut. The smart thing to do, however, is to look at what is going on underneath the headlines.