The near future.
Exactly how far into the future is ambiguous, but it generally refers to anywhere from five to fifty years. Far enough into the future to be noticeably different from the present, but not far enough to be unrecognizable from the present.
Can also be "twenty minutes into the future", "five minutes into the future", and so forth. In this context, "two weeks" (or "twenty minutes" or "five minutes") is exagerrated the same way "that is so five minutes ago" is an exaggerated way of saying something is days or weeks out of date, or "this is taking all day" is an exaggerated way of saying something is taking too long.
"I just read a really good science fiction novel. You should check it out if you're into that sort of thing."
"Is it really futuristic, like Star Wars? With flying cars and ships and laser guns and laser swords? That kind of stuff?"
"No, it's more of a 'two weeks into the future' sort of thing."
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