THE claim that Labour voted with the Conservatives for £30billion of spending cuts in the next parliament has become a staple of the SNP election campaign. No speech, no press release, no TV clip is complete without the story of how Labour MPs "trooped through the lobbies" shoulder to shoulder with the Tories to back George Osborne's austerity plan.

By quite some margin it is the biggest porky of the campaign. What MPs voted for in January was the Charter for Budget Responsibility, which commits the government to balancing the current budget, or day-to-day spending, over the next parliament. The Tories claimed the next government would have to make additional tax rises or spending cuts of £30billion to meet the target. But the charter itself puts no numbers on what might be required. The goal is consistent with Labour's pledge to eliminate the deficit and Ed Balls, the shadow chancellor, says it can be achieved by a much smaller fiscal consolidation and higher economic growth. Labour viewed the charter as something of a gimmick but had no problems supporting it.

Labour's abject failure to rebut the SNP's claim says a lot about the party's effectiveness right now. It says even more about the power of repeating a line over and over especially if you have a receptive audience, as the Nationalists do. "I challenge this every day," said one Labour candidate ruefully. "It is dishonest and disingenuous to suggest we voted for £30billion of cuts but it has become an article of faith for the SNP."

The claim has never stood up to even the most cursory scrutiny. Why, if Labour and the Conservatives were supposedly on the same page economically, would Nicola Sturgeon rule out a deal with one and pursue the other as a potential post-election ally?

As with so much election hokum, the idea was finally demolished this week by the Institute for Fiscal Studies.

The independent think tank, whose expertise and integrity is acknowledged across the political spectrum, compared manifestos and concluded overall public spending on services up to 2019/20 would be slightly lower under the SNP's proposals than under Labour's. The SNP plan would also result in a small cut to Holyrood's budget, contrasting with a rise under Labour, according to the IFS.

John Swinney quibbled about some of the think tank's assumptions but taking those board would not alter the big picture: the SNP's plans are very similar to Labour's and those two parties are a long way apart from the Conservatives.

In a stinging aside, the IFS said the Nationalists' "stated plans do not necessarily match their anti-austerity rhetoric." The rhetoric, however, seems to be working. Having dismissed the IFS study as "not credible" the SNP will continue to promise an "end to austerity," to go further than the "limited alternative proposed by the Labour party" and to make an Ed Miliband minority government "bolder and better".

In the long run, however, when we return to the real world after after May 7, the similarity between the Labour and SNP plans could prove significant. It would make it hard for the SNP to oppose a Labour budget and easier for Ms Sturgeon to become a constructive ally for Mr Miliband, as she has promised, if the parliamentary arithmetic puts him into Downing Street without a Commons majority.

That is where she is happy to be. In an interview with The Herald yesterday, the First Minister made a comment which revealed much about her strategy.

Dampening expectations of a swift re-run of the independence referendum, she said SNP members were a "pragmatic bunch" who understood that Scotland would be not rushed into a second vote. Many of those members voiced agreement on social media, insisting they did not want a referendum until they could be sure of victory. Despite the party's soaring fortunes that could not be guaranteed. As the row over full fiscal autonomy has shown, unless something dramatic happens to the price of oil, the SNP would have to fight any rematch in the foreseeable future with a weaker economic case than it had last year.

In these circumstances, it is in Ms Sturgeon's interests for a minority Labour government to succeed. An effective Miliband government, backed by the SNP would render Labour unnecessary in the eyes of many Scots voters. It would consolidate the huge gains the SNP looks set to make. And if the SNP can reduce Scottish Labour to a rump, replacing it as Scotland's dominant party at every level, the chances of winning an independence vote would soar.