Short of a massive Vita price drop coming within the next... 2 weeks... I doubt it. At least until the generation is winding down.

Without GTA, God of War and a pricecut? I highly doubt.

It could have good weeks, good months, but it's not going to be something usual.

Short answer: No.

Longer answer: Not a chance in hell.

If PSP could barely manage half of what DS/DS Lite/DSi sold, what chance does the Vita, which has had a MUCH slower and more abysmal start, actually have of ever overtaking the 3DS? None.

Not this year, Vita has some interesting stuff coming out, but even with a price cut I can't imagine it doing better because it doesn't have any games that will even compare to when pokemon hits.

Next year it could match it at most, but that requires a lot of things to happen. I think next year won't be as good for the 3ds, unless the Wii U utterly fails enough that Nintendo returns full focus on it. Also, Vita would have to have a lot of system sellers coming for it, another Uncharted and Assassins Creed, a good COD, God of War, GT, GTA. I don't think there is any chance it will beat it next year either though.

Maybe it could beat it in 2015.

Maybe one week (when the price cut happens)

One problem. Nintendo has a deal with campcom and capcom can only release monster hunter games on nintendo's consoles.

Here is what I think:
~ Price cut - Will make the PSVita outsell the 3DS for that week, of course.
~ Week after Price Cut - PSV will still outsell the 3DS. (Unless Nintendo ends up releasing a game around this time, I doubt it, though.)
~ 2 Weeks after the Price Cut - This is when the PSVita will start to drop off in sales quite a lot. It'll still outsell the 3DS this week but the next week I seriously doubt. (I'm basing this to where Sony would drop the price around September. If the Price is dropped sooner than September then we will most likely see the PSV outsell the 3DS for almost a month, maybe a little more.)

This is all speculation. I don't know Nintendo's SW Release Schedule all too well and I don't know when Sony will drop the PSV's Price.

Do you have a source confirming this?

^ I don't buy it. The Vita isn't even outselling the 3DS the week of the price cut in Japan. 3DS is weaker in America, but by summer it'll be doing much better. I'll give Vita 2 weeks, maybe 3, if it gets its price cut before Pokémon. After Pokémon? One week at most.