... (some time between fall '63 and spring '65) I wrote a short story with a similar premise:
The government's physicists had identified a way to create such a "bounce" situation by a nuclear mumbo-jumbo that starts with putting together a dense enough energy packet. This backs the universe up a bit and it takes another alternative timeline. Humans have just enough psi to make different decisions. The more energy you use to start the process, the farther back the "time bounce" to the fork. Or at least that's the theory.
The government has taken advantage of this by creating a secret project: They are collecting and storing a LOT of energy using a solar power satellite. (The downlink is a laser and the ground-based collector and energy storage tech, like the details of the bounce device, are unspecified.) Accumulation of energy is ongoing, so they continue to have enough to bounce back at least to the time when the project was initiated. (Going farther risks taking a fork on which the device is not made.)
This is used by the diplomats as a way to correct mistakes: If things got too bad diplomatically they could go back and try something different. (Unlike a doomsday device you WANT to keep this one secret - and for there to be only one.)
Since the project went online, though there have been many conflicts and near-misses on situations with the potential to degenerate into something that would make WW II or a comet impact look tame, things have always worked out for the government in question. Sometimes by smart diplomacy, sometimes by smart battle strategy in small conflicts heading off large ones, sometimes by seemingly amazing coincidences and blind luck. Starting as one country on Earth (where the device is still sited) the government has (mostly peaceably) unified/absorbed/explored/grown into a multi-solar-system empire.
The kicker is that, from the viewpoint of the operators (from which it is was written) EVERY use is the FIRST use. It ALWAYS appears that things have miraculously gone so well that they haven't needed it - until JUST NOW. Maybe the thing really doesn't work - in which case it will destroy the planet and life on most of the spiral arm. Maybe it does work - but from the viewpoint of the current timeline it's just the end of the universe. Maybe the diplomats and generals, knowing this is a possibility, have gone to heroic efforts and pulled out heroic saves - until JUST NOW. But now it's finally hit the fan and the viewpoint characters have been ordered to set it off ...
One of the others in that class was the guy who was the model for Aahz in Asprin's books. Ran into him a decade or two later. He brought up the story and said it had haunted him ever since. B-)