'When my boat comes in' is a variant of a legal phrase used in the Court of the Admiralty as long ago as the 1500s. The concept behind it is pivotal in the plot of Shakespeare's 'Merchant of Venice', for example.
The suggestion is that the arrival of one's "boat" signals the making of one's fortune...ie lots of money coming in. In the same way, 'to push the boat out' is to get involved in paying lots of money out. The latter is little more than an inversion of the former.
The fact that there is no recorded use of the phrase prior to the 1930s certainly suggests that it is quite a recent coinage.