You asked how? I suppose through extensive and ongoing queries, but don't hold your breath...
Theoretically you could find someone (an owner or their property manager) who is BTB licensed for vacation rentals that would be "willing" to accept such a rate. But the realities of that are very very slim at best. Frankly as an owner I don't see that happening given the cost of vacation rental upkeep. All "vacation rentals" are subject to the 9% BTB tax. If you do the math on a $1000/month, BTB tax included, the pre-tax monthly rate would have to be $917/month ($1000/1.09) or about ~$30/day for a 30 day month...
To expand on Simons comments: A possibility does exist when a sublease of a long term rental is legally available at such a rate, I say legally because not every long term lease allows subleasing and you have to be very careful to not create an exposure for eviction. You're going to want to see the original lease to ensure the sublease is allowed and evidence that the owner approves. That's all going to need to be brokered by the agent who handles the long term lease to begin with. As Simon pointed out, landlords or their property managers, aren't going to be willing to take on that screening hassle for such a short period unless the circumstances are exactly right (e.g. its the first or last month of a long term lessors term and they need someone to stop gap that time).