There are two reasons why the PLP revolt against Jeremy Corbyn's leadership is unlikely to succeed. The main reason is that the Parliamentary Labour Party will be unable to avoid a leadership election without Jeremy Corbyn (or John McDonnell in the unlikely case that Corbyn decides to step aside) on the ballot. While possibly legal, the unions are, mildly put, opposed to such a maneuver, and while the National Executive Committee seems split down the middle, it is difficult to conceive Constituency Labour Party representatives voting against giving members a vote. Running the leadership election without Corbyn would amount to rerunning the EU referendum without a "Leave" option. It would be seen as undemocratic and its legitimacy would be difficult to uphold. While one could argue that ignoring the decision of 17 million voters would be worse than ignoring the decision of 250 thousand Labour members, Labour members or NEC member would be unlikely to agree with such reasoning.
The second reason why the PLP revolt will ultimately be unsuccessful is that in order to win a leadership election, the candidate nominated by the PLP would need to win over wavering 2015 Corbyn voters and attract new, moderate Labour voters to join the party. Angela Eagle, if confirmed, is not the right candidate to do either. On many issues salient to Labour members, be it Iraq (which coincides with the Chilcot report next week), Trident, or Syria, she is far to the right of members. Attacks write themselves. These issues are salient to Labour members, and Labour members are the selectorate that will decide whether Corbyn stays. Eagle is not particularly popular among Labour members. She finished 4th out of 5 in the deputy leadership election, behind Caroline Flint, Stella Creasy and Tom Watson. To make matters worse, her own CLP strongly backs Corbyn.
Neither is Eagle, even if strongly supported by the PLP, likely to create the enthusiasm necessary to out-mobilize the Labour left in the recruitment of new Labour members by a margin wide-enough to make up for her likely failure to persuade Corbyn backers to switch. While she is a seasoned Commons performer, there is nothing to suggest that she is particularly liked among Labour voters. In a post-referendum YouGov poll commissioned by Citi she only gained 1% when Labour voters were asked who would best replace Corbyn.
It is therefore totally inconceivable how the PLP could think that Eagle would stand the best chance of winning a leadership contest against Corbyn. The failure to recruit Lisa Nandy, Gloria de Piero, Owen Smith or any other Labour MP who is untarnished by the Blair years and could make a plausible case of being in sync with members will ultimately spell defeat.
A likely defeat of the PLP revolt may ultimately lead to the break-up of the Labour Party with a majority of MPs and a minority of CLPs probably leaving to found a new centre-left party. This outcome, which now seems likely, was entirely avoidable. Even following the logic of PLP rebels, it is difficult to see how splitting Labour into two is more likely to lead to a centre-left government than replacing Corbyn after an early General Election. While Labour might have lost this election, it is unlikely to have suffered as many losses as it is likely to suffer in the wake of a party split.