Just because you'll have 1,001 lives to clear the less-than-OSHA-complient pathways in 1,001 Spikesdoesn't mean you'll eventually get through them. Teaming up with friends would certainly help diversify your survival odds, or at least supply emotional support as you're torn apart by ancient deathtraps, but that social safety net won't be strung for Vita and 3DS players. A recent tweet from developer Nicalis states that 1,001 Spikes "will not have multiplayer" on either handheld.
If you're still planning on braving the journey on the 3DS or Wii U, know that the first few days of your treasure hunt might be a little buggy. Still, Nintendo has assured Nicalis that a patch could be issued "within a couple days of release" to fix any issues that arise with the experience.