In politics, the short answer ought to be no. The Sun's much vaunted 3 million readers don't look to it for political guidance; most of them are thoroughly uninterested in politics, and many won't bother to vote. However, the Sun does have a huge influence as a weather-vane newspaper - it generally manages to support the winning party at every election, by carefully following popular opinion. Not that it will have taken a great deal of political insight to gamble on Labour losing the next general election.
What hurts is the timing of the announcement that they are no longer supporting Labour, and some observers are putting this down to the influence of former News International employee Andy Coulson, now David Cameron's Director of Communications. What is also likely to be the case is that Rupert Murdoch, the Sun's owner, is hoping to exact useful political capital for turning his paper's support to a man he once described as 'lightweight'. Whatever the Sun does, it isn't for political conviction, of that at least we can be sure!