Will the cuts move opinion to the left?
Yesterday the latest figures from the British Social Attitudes survey were released, with most of the media attention focusing on the findings that support for the government spending more money on benefits and the government redistributing income have both dropped to lower levels than in the 1980s (27% support the former, 36% the latter).
Polly Toynbee's column in the Guardian today predicts that opinion will shift back in the opposite direction once public spending starts falling, unemployment rising and so on. The column produced something approaching ridicule in the comments section over on politicalbetting, but on that specific point Polly is probably right.
We certainly can't accurately predict how patterns of party support will change in response to rising unemployment (and since I'm no economist, I wouldn't predict levels of employment either!), you can't really be sure about how public opinion on individual issues and measures will shift. What we can do is look at the broad left-right positioning of public opinion and how the "centre ground" moves from left to right (or vice-versa).
In Britain at the Polls 2010, John Bartle has aggregated together all the suitable tracker questions from polls since 1938 (a total of 4,236 questions) and coded responses as being left wing or right wing. This produces an average left-right position for the public each year, expressed on a scale from 0 (very right wing) to 100 (very left wing).

Above is how this political centre has shifted around since 1950. As is self-evident, public opinion gradually moved rightwards during the 1960s and 1970s, then switched and moved steadily leftward throughout the Thatcher-Major government, before moving to the right again under Tony Blair and Gordon Brown. For the last two governments the correlation is pretty much perfect - under a government of the left the public react by moving to the right, under a government of the right the public react by moving to the left. It doesn't seem to work quite so well pre-1979.

The second graph is the same line, but reversed (so left is now at the bottom of the scale and right at the top), and compared to public spending as a percentage of GDP. The match isn't so perfect as spending as a % of GDP jumps about a lot in response to recessions and booms, but there is still a clear relationship - as public spending rises, people react by becoming more right wing, as it falls people become more left wing. Underlying public opinion essentially operates like a thermostat... as public spending rises, more and more people switch to thinking that the state taxes and does too much. As it falls, more and more people think the government should be re-distributing more, spending more on public services and so on (of course, most people don't have a clue how much the country actually spends as a percentage of GDP. What changes opinions on an individual scale will be people's own personal experiences.)
On the basis of how public opinion has moved over the last 30 years, we can legitimately expect public opinion to start moving leftwards now there is a government of the right in power reducing the amount of money spent by the state. On that basis, Polly is right. What we can't conclude is that this will necessarily be some great boon for Labour, elections are about a whole lot more than left-right positioning, they are also about the leaders, party images, perceptions of competence on important issues and so on. Britain started moving leftwards in 1980, but it took a further 17 years for Labour to win back power; it started moving right in 1997, but it took 13 years for the Tories to return.
(Thanks to John Bartle for permission to reproduce his numbers)