The two debates seem likely to collide anyway, since Boehner told his conference on a call last week that he plans to push for a stopgap continuing resolution to keep the government funded at lower spending levels than Obama would like.
Of course, if lawmakers were able to reach a longer-term agreement in October, that could save members of Congress and their staffs from spending another holiday season in the Capitol, as has become the normal practice in recent years. Both chambers were in session on New Year’s Day of 2013.
Emma Dumain contributed to this report.
Correction: 8:16 p.m.
An earlier version of this article attributed a sentence to Treasury Secretary Jacob J. Lew that was not in his letter. The following was not in his letter: The upcoming spending debates on Capitol Hill will almost converge, setting up a tough slog in September and October.