I'm not sure I agree with this. The Rainbow Coalition under David Milliband (probably) would likely be more coherent than you think. First and foremost, all the parties would be aware of the immediate consequence of a break-up, an election and a Tory majority.
Am I suggesting Lib Dems in the Cabinet ? No, I don't think so and not with Nick Clegg as LD leader though I do see widespread consultation on policy especially on electoral reform and a not very subtle attempt to prevent a Conservative landslide.
Of course, degrees of support will vary - some parties may simply offer support on Supply & Confidence. Others may choose more active involvement. The key players are Labour, LD and the Nats. Caroline Lucas doesn't matter that much and as long as the SDLP/Alliance and Lady Hermon stay onside the Rainbow will have enough votes.
I don't think it would, Stodge. For example, what happens with Tuition Fees? I think it's pretty improbable Labour wouldn't implement the findings of their own Browne Report, and, given the Tories won't be
at all co-operative on that, and the Lib Dems won't vote in favour, the Government will be defeated.
In addition to this, people generally voted for the "other than Conservative" parties in the expectation there wouldn't be any cuts. We've seen just how badly that incorrect perception has impacted upon the Lib-Dems. ITTL, we'll see it impacting upon Labour too, and the other parties. Lucas certainly will vote against cuts, and I suspect the nationalist parties will veto any cuts in the Scottish, Welsh, and NI budgets, which will mean deeper cuts in England. All of this will hit Labour's popularity very badly indeed.
Finally, there's the whole thing about legitimacy. Look how people complain about Cameron's legitimacy IOTL- and that's with him as leader of the party that won the most votes and seats, and leading a Coalition that won nearly 60% of the vote. Miliband, by contrast, will be a second unelected Prime Minister, leader of a party that was clearly defeated at the polls. The Rainbow Coalition will be seen as totally illegitimate, even more so than the current OTL one is.
I'd expect to see opinion polls throughout the lifetime of the Rainbow Coalition hovering somewhere around
10/25/50. When an election is eventually called, these will obviously be whittled down somewhat, but I stick to my prediction that it'd be a comfortable Conservative victory, with a majority of fifty or sixty seats at minimum.