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Theresa May can't just unilaterally call a General Election. As mentioned upthread, a majority commons vote of 2/3rds is needed to trigger one.
However, in the wake of the referendum she is very well placed to secure one. The Conservatives will all vote for it and, in order to get a post-brexit indyref back on the table, the SNP will most likely vote for it. That leaves Labour, Lib Dems and the minor parties. Based on previous post-brexit posturing, there's a fair few Labour and LD MPs that would have a hard time opposing it. Might be a narrow margin but that 2/3rd target is well within the realm of possibility.
Alternatively, if it doesn't get passed the 2/3rds, it legitimises the current government until the end of their term unless there is significant material change. Labour sorting out their leadership issues doesn't count.
At least that's one Trident supporter out of the race.
I suspect Smith's anti-Brexit stance will garner him a small surge un supporters but I can't see him beating Corbyn.
Cue a snap election from May and another five years of Conaervative rule courtesy of Labour being a bit shit.