Both are set for September 30, when House Republicans can both cause a government shutdown (as Stan Collender explains) and force the gas tax to expire unless whatever demands they can think of are met.
By the way, there is no need to limit these demands to spending cuts. There will probably lots of unrelated demands as well. (Healthcare, oil drilling, reversing other regulations they don't like, any tax changes such as a dividend holiday that they happen to favor, etcetera.)
Given what happened the last time around, what would be the argument within Republican circles against playing these to the hilt? After all, neither involves threatening to destroy the full faith and credit of the U.S. government. And even if Obama genuinely plans to stick to his guns this time (not that I'd actually expect him to, closer to zero hour, even if he sincerely believes that he will), how could he possibly communicate this credibly to the Republicans?