A win would help to calm those on his backbenches who worry he is not the right man to lead them to an outright victory at the general election in 2015.
If he can win here, all the concerns among traditional Conservatives over Europe, gay marriage and the faltering economic recovery will be put aside - for a time at least.
Lose to the Lib Dems and that resentment will continue to grow.
The majority (3,864) is not insurmountable - but this is an election in which one side of the unpopular coalition is fighting the other. How to be united nationally and yet picks fights locally?
And given their association with the Tories in government, the Lib Dems are keeping this fight local.
You hear them talk about council tax and housing, not the national deficit and spending cuts.
The truth is, the Lib Dems are very strong in this corner of Hampshire. In the bit of the local council which mirrors the constituency, the party has 36 out of 36 councillors.
It is why the Lib Dems are the bookies' favourite to succeed here. Just.
This former railway town should have a strong Labour base but the constituency takes in some pretty yachting villages along the River Hamble and some large housing developments on the outskirts of neighbouring Southampton.
As for UKIP? I maintain party leader Nigel Farage would have shaken up this campaign had he decided to stand. His party is likely to get a much better result than in 2010 but I don't yet see any signs that this by-election is going to yield UKIP its first MP.
So in the constituency in which the Spitfire took its maiden flight before the Second World War, the Battle of Eastleigh is now under way. This will be a Cameron vs. Clegg contest and one of them will have to deal with the consequences of losing.
Both their parties expect.