Has the SNP peaked?

Can Alex Salmond walk on water indefinitely, or is he about to sink under the weight of his own ego and his links to Rupert Murdoch? As Scotland's voters go to the polls today in the local elections (well, a few of them anyway) the question on everyone's mind will be: is the SNP slipping, has the magic gone, is Alex Salmond mortal after all?

Expectations were high, stratospheric even, following last year's Holyrood landslide for the SNP. If the Nationalists don't take Glasgow and Edinburgh tonight then the commentators will be saying it's the beginning of the end – even if it isn't. Glasgow is a big ask, and Labour has poured effort into saving its citadel. My own view is that Scotland's love affair with Alex Salmond hasn't ended yet, though the relationship could do with a bit of counselling.

Now, I should of course be stressing here that local elections are supposed to be about local issues: refuse services, potholes, local sleaze, trams and so on. But they rarely are. The electoral system anyway makes it very difficult to vote on local issues because PR generates shifting coalitions. How do Edinburghers express their fury at the trams fiasco when all the main parties are implicated one way or another, with the exception of the Tories perhaps? In the absence of elected mayors – identifiable, buck-stopping civic personalities like Ken and Boris in London – local voters tend to use their votes to pass a verdict on the state of the national government.

All governments lose political momentum eventually: the media gets bored, scandals start chipping away at the leader's credibility, voters start to blame the government for economic misfortune. And by rights this should be happening to the SNP. The Scottish Government is no longer driving the legislative agenda. Indeed, right now it's difficult to say what the SNP Government is there for other than to prepare the ground for the independence referendum in 2014.

It was very different at this stage in the last parliament when hyperactive SNP ministers were busy replacing PFI, saving accident and emergency units in hospitals, abolishing charges on things like prescriptions and bridges. The 2007 SNP administration had moral purpose coming out of its ears – condemning the war in Iraq, opposing nuclear weapons in the Clyde, tackling climate change and introducing the toughest CO2 emissions targets in the world. Latterly it defined itself through opposing university tuition fees, promoting growth in favour of austerity and legislating for minimum pricing on alcohol.

It was that sense of purpose and conviction that allowed the SNP to sail through the 2008-10 financial crisis largely unscathed, even though Alex Salmond had been far too close to individuals such as Fred Goodwin and had been allowing his speeches to sound like press releases from RBS. Labour has never understood why it got a lot of the blame for the financial collapse and yet gained none of the credit for the banking rescue which was organised by a Labour Chancellor, Alistair Darling. Why hasn't Mr Salmond been tainted forever as the bankers' little helper?

Only now has Labour begun to develop a narrative that revisits the banking crisis and seeks to put the SNP leader, retrospectively, in the frame. Alex Salmond, say Labour, is over-enamoured of rich men. Look at the way he volunteered to lobby for Rupert Murdoch on his bid to take over BSkyB? Look at how eager he was, initially at least, to back loud-mouth Donald Trump's golf-and-property deal on the Menie Estate? How he has accepted large sums of money from Brian Souter, the fundamentalist Christian who bankrolled Keep the Clause. Alex Salmond, say Labour, is a soft touch for any plutocrat who offers a donation or favourable treatment in the press. Look how he is refusing any inquiry into phone hacking in Scotland, and insisting it should be left to Leveson in London.

Labour is on the right lines here. It hooks into suspicions that Salmond has too much control over his party, parliament and the country. Don't let him dominate local government as well, warn Labour. However, though plausible, the message is premature and fails the "yes, but" test. After all, is it not Labour that has controlled Glasgow for the last 80 years, with uninterrupted rule for the last 32? If ever there were a need for a change, it might seem to be in Scotland's largest city, where the Labour years have recently been defined by scandal, division and indifferent governance.

The SNP's group leader, Allison Hunter has rather queered the pitch by suggesting that Glasgow is just a "stepping stone" to independence. But I suspect that uppermost in the minds of many who vote today will be the desire to see change in the way the city is run, and installing a new SNP broom is the best available option. Moreover, most voters accept that First Ministers have to deal with rich individuals like Murdoch and that Labour are hardly in a position to criticise, since they've been in bed with Rupert Murdoch too. Tony Blair flew halfway around the world in 1996 to appeal for the support of the Sun King.

So, I don't expect to be pronouncing the beginning of the end for the SNP tomorrow, but there is a definite air of drift. Alex Salmond is still a hugely popular leader, but his weaknesses are becoming exposed as his government struggles to define itself in the second term. Being the party of the referendum is all very well, but the SNP must always remember that Scots didn't vote for them because they wanted independence, but because they wanted a better government in Holyrood.

There is a huge risk in appearing to follow leaders such as Tony Blair and David Cameron into the arms of Rupert Murdoch. It may not be an issue on the doorsteps but that doesn't mean people are happy with the First Minister appearing to lobby for the newspaper tycoon. Rightly, they expect better.