Tony's push for further CAP reforms came from Chirac's calls for an end to the British rebate, as far as I recall. The CAP was reformed in 2003, but the mid-term review is still imperfect. I'd prefer to have the first pillar completely ditched, compensated by a moderate expansion of the second pillar (rural development) and a regulated allowance for Member States to compensate their farmers for services of general economical interest.

But it's perhaps more likely that first pillar reforms will (continue to) make it more like the second pillar (e.g. national co-financing of the direct payments indexed by regional wealth; more cross-compliance with environmental and social standards; a cap on per-farm payments). Which would also be workable. I don't think that such reforms would lead to less popularity for the EU overall. It will become more popular in some areas and less popular in others.

The current reality of the CAP necessitates further reforms, because the policy will soon no longer be able to fulfil the objectives nations like France and Germany have of keeping their countrysides vital, due to a decreasing cap on total payments coupled with an increasing share paid out to the East European countries. Because any attempt to increase the cap will be resisted by the countries that pay for the EU, partial or complete renationalisation of the first pillar (as in two above scenarios) is the only way out.

It will also be more likely to happen, with Chirac soon out of office. Ségolène Royal has already proposed something roughly in line with the partial renationalisation I described above (see speech).