The newly-installed "leader" of Labour's branch office in Scotland made clear during the campaign that as far as he was concerned he was also running to become First Minister. But will Murphy even get to the point of submitting himself to the voters on that basis in May 2016? I can think of at least four ways in which he might be dislodged before then...
1) He might stand in East Renfrewshire at next year's general election and be defeated. People quite naturally talk about Murphy's personal vote and the bonus he may get from his visibility as "leader", but both of those points are already factored into the 2010 baseline result, which saw Murphy as the incumbent Scottish Secretary defeat the Tories by more than 10,000 votes in a constituency that in its "wild state" ought to have been either a safe Tory seat, or at best a Tory-Labour marginal. So there's no obvious reason to suppose that he'll be enjoying a personal advantage over and above the one he had last time, which means that the following figures are entirely relevant -
Swing required for the SNP to defeat Murphy : 21.0%
Current national Labour-to-SNP swing implied by the Poll of Polls : 20.3%
Swing required for the Conservatives to defeat Murphy : 10.2%
Current national Labour-to-Conservative swing implied by the Poll of Polls : 7.8%
It looks a bit close for comfort on both fronts. Yes, the likelihood is that the SNP's national lead over Labour will at least reduce as polling day approaches, but I don't see how anyone can ponder the above figures and conclude that East Renfrewshire looks at this moment like a shoo-in for Labour. If Murphy were to lose, it's not entirely clear to me whether he would be automatically required by the party's rules to relinquish the leadership - but his position would surely be untenable anyway.
2) He might resign as an MP, stand in a Holyrood by-election and be defeated. We all know that by-election campaigns can be as mad as a bucket of frogs and produce stunning upsets, and you can guarantee that the SNP would throw the kitchen sink at this one. Murphy might seek to avert the "by-election bubble" problem by engineering a contest to take place on the same day as the general election, but then he would risk being carried away by a nationwide SNP tidal wave - if the current momentum continues (which is admittedly a big if).
3) He might take the rap for heavy losses to the SNP next May, even if he wins his own seat. In theory, there's no particular reason why he should take the rap, because Ed Miliband is the leader in Westminster terms and Murphy will only be playing a support role in the general election campaign. But it's Murphy himself who has chosen to personalise this by repeatedly claiming that he will ensure that Labour retains every single Westminster seat that they currently hold. He might be able to gloss over the loss of Falkirk and one or two other seats, but if the carnage is as great as the opinion polls currently suggest, the media will be in a position to recite his words back to him over and over again and make his leadership look like an abject failure. (Although the million dollar question is whether the media would actually choose to put him under that kind of pressure, because the likes of Kenny Farquharson seem to have a rather sweet crush on Jackanory Jim.)
4) He might not be able to resist standing for the UK Labour leadership if a vacancy occurs next year, or he might be tempted by an offer of a senior Shadow Cabinet post from Miliband's successor. It's no secret that Murphy sees his native country as a backwater, and would never have dreamed of heading to the Scottish Parliament if his career prospects under Miliband hadn't looked as bleak as they did. But if Labour are defeated in the UK general election, the situation will change, because Miliband will almost certainly no longer be leader. Assuming Murphy is still MP for East Renfrewshire, he would be eligible to run for the UK party leadership, or to return immediately to the Shadow Cabinet in a senior role if another Blairite becomes leader. Yes, he'd know that would leave the Scottish party in a state of utter chaos, but let's be honest - if he no longer has a personal investment, do we really think he would care?