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Having won his stay of execution from his own supporters, Gordon Brown begins the struggle to redefine and rehabilitate himself today among the wider public, with plans to "clean up" politics and talk up the case for wider constitutional reform. It will be interesting to see how long this new show stays on the road.

Cleaning up politics should be the easy bit since there is enormous public support for it and a measure of all-party consensus. But it remains to be seen if the public will trust those who presided over the abuses (looking the other way until disclosure forced them to confront the scandals) with the clean up. The danger for the PM and the government is that both are so thoroughly discredited in the public's eyes () that voters won't believe a word they say ().

Nor have things got off to an auspicious start. , who was forced to quit as a minister pending an investigation into his expenses, has just been reinstated because the investigation has apparently cleared him. I say "apparently" because the report into his expenses is not to be made public so neither I nor you can really tell. So much for all these promises of a new transparency.

Nor is it clear how big the appetite is among voters for constitutional reform. In the midst of a terrible recession and with so many MPs being seen to have their snouts in the trough, I'm not sure people's minds automatically turn to the case for , fixed term parliaments, an elected Lords or any other of the constitutional wheezes currently reverbating round the Westminster chattering classes with renewed enthusiasm.

It could be the most striking example yet of how the Westminster village is often in another country from the folk who put them there. Most people, I humbly suggest, want honest politicians and to know that their job and homes will be secure in the current downturn (and if they're not, what the government is doing about it). A rarified discussion on the merits of AV versus STV voting systems might not quite catch the public mood.

I suspect the whole thing will also be greeted with a certain public cynicism. After all, the government has flirted regularly with electoral reform but never come close to consummating it. And there have already been several reforms of the Lords, which seems to be a never-ending process rather than an end-game. Voters are likely to ask what the government could hope to achieve in a year that it has not managed in 12.

Time is a serious constraint: the Brown government . Parliamentary expenses can be cleaned up in that time but, with the best will in the world, it is hard to see how any important constitutional reform could be implemented in that time. Nor is it clear that it should be: constitutional reform should always be considered and unrushed, done after much contemplation and widespread national debate.

Voters who see a government rushing to re-brand itself with such reforms might not think the Brown government quite fits the reforming bill.

³ÉÈË¿ìÊÖ News' Laura Kuenssberg reports on the possible changes to voting systems, and how they have been used in Welsh, Scottish and London elections:

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