A picture, so they say, paints a thousand words, or in this case a poster does. Rarely has a general election billboard generated such an impact. Many have been memorable – think 1979’s “Labour Isn’t Working” – but none have provoked such a direct response. Ever since it first appeared just over a week ago, a cry went up both within and outside the Labour party that “something must be done”. And, as the rest of the politician’s syllogism has it, ruling out a coalition with the SNP was something; therefore, Ed Miliband had to say that.

But, as the Scottish first minister Nicola Sturgeon put it yesterday afternoon, “a lot of hype” surrounded the Labour leader’s decision to rule out “something” that no one was actually proposing. “There will be no SNP ministers in any government I lead,” said Miliband. Fine by me, was the SNP leader’s nonchalant response. For Sturgeon has consistently spoken of her “instinctive” preference for supporting Labour on an issue-by-issue basis rather than via a more formal arrangement. In the circumstances, however, it was the only “line” Miliband could have chosen.

There is genuine anger within the Labour ranks about the Tories’ divide-and-conquer strategy

This at least gives Labour a reasonably solid position in the weeks remaining until 7 May. “We won’t coalesce with the SNP” has the merit of sounding decisive without actually being a hostage to fortune, but for those out of the Westminster bubble – the majority of voters – it will sound credible enough.

Only it does not, of course, completely negate the Conservatives’ implication that a Labour government could be foisted upon middle England with the help of a party dedicated to breaking up the UK, for it leaves open the prospect of a “confidence and supply” arrangement if not a coalition. If Miliband had ruled that out too, then he would effectively have been waving goodbye to any prospect of becoming prime minister.

There is genuine anger within the Labour ranks about the Tories’ divide-and-conquer strategy, which they regard as cynical and incredibly damaging to the wider unionist cause. On one level it is Lynton Crosby-inspired genius: focus groups have revealed that Alex Salmond, though still wildly popular north of the border, is markedly less so south of Berwick-upon-Tweed.

Thus posters showing Miliband poking out of an oddly statesman-like Salmond’s top pocket conjures up images of a constitutional bogeyman, either a formal Labour/SNP coalition or what the Conservatives describe as the “worse” scenario of a less formal arrangement. Either way, runs the argument, Labour will be dancing to a nationalist tune.

While that plays well (from a Tory perspective) in England, it, ironically, also suits the SNP in Scotland, where they’ve been talking up precisely that electoral outcome. It’s clear (thus Labour’s anger) that Downing Street cares little that this can only shore up the nationalist vote, for the prime minister obviously wants to secure a second term so badly that the constitutional consequences of his strategy are considered a price worth paying.

Although the SNP is naturally delighted at how all of this is playing out, its position vis-a-vis Labour is shot through with contradiction. Sturgeon is dedicated both to destroying Labour in Scotland and propping it up in England; speaking at the London School of Economics on Monday she even urged English voters to back the Greens rather than Ed Miliband’s party.

All of this, however, serves to highlight Labour’s weakness, not only (and most severely) in Scotland, but also south of the border, as they feel compelled to issue statements because of a billboard poster.

The phrase “a picture paints a thousand words” was apparently first used in 1921 by the ad-man Frederick R Barnard, who commented that graphics could tell a story as effectively as a large amount of text. In the midst of a high-stakes general election campaign, UK politics has produced a textbook example.