How much room for renegotiation did Cameron have prior to the EU referendum?

Prior to the EU referendum last year, David Cameron attempted to renegotiate the terms of Britain's membership with the leaders of other EU member states. Many commentators (though not all) regarded his renegotiation as a failure, arguing that he achieved very little of substance. It is therefore interesting to pose the question, could he feasibly have obtained more concessions from other EU leaders?

I came across some interesting polling, which suggests the answer is almost certainly not. In February of 2016, Lord Ashcroft polled citizens of all other 27 EU member states. First, he asked them:

As you may know, the United Kingdom will have a referendum within the next two years to decide whether or not to remain a member of the European Union. Would you prefer to see the UK remain a member of the EU, or would you prefer the UK to leave, or does it not matter to you either way?

Results were as follows:

A majority in almost every member state said they would prefer the UK to remain a member of the EU. On average, 60% answered "Remain", 30% answered "Doesn't matter", and only 10% answered "Leave". However, Lord Ashcroft also asked EU citizens:

The UK Prime Minister, David Cameron, is negotiating with the leaders of other EU countries to change the terms of the UK's membership of the EU. Which of the following statements comes closest to your view? It is important that the UK should remain a member of the EU. If the UK does not like the terms of EU membership it should leave.

Results were as follows:

A majority in most member states said they would prefer the UK to leave the EU, rather than to renegotiate the terms of its membership. On average, 57% answered, "If the UK does not like the terms of EU membership it should leave", while only 43% answered, "It is important that the UK should remain a member of the EU".