So after burning $15 on a watt meter, the 22 year old 2.5hp Craftsman came in at >1150W starting & 900W constant power.  The internet may differ in opinion, but $100 inverters these days are rated for 2KW peak & 1KW constant power.  

https://www.harborfreight.com/1000-watt-continuous2000-watt-peak-modified-sine-wave-power-inverter-63522.html

There's also a 1.5KW/ 3KW peak one.

https://www.harborfreight.com/1500-watt-continuous3000-watt-peak-modified-sine-wave-power-inverter-63432.html

The mane problem is $100 of LIPO would provide 1kW for 14 minutes of vacuuming before the batteries were destroyed.

https://hobbyking.com/en_us/turnigy-5000mah-3s-20c-lipo-pack-w-xt-90.html

$100 of deep cycle lead acid would last 1.4 hours, but this would take up the entire apartment just to do 1 thing.  

https://www.walmart.com/ip/EverStart-Lead-Acid-Marine-RV-Deep-Cycle-Battery-Group-Size-29DC-12V-845-MCA/20531543

This is still cheaper than what a gasoline generator would cost.  Gasoline generators don't have a peak & constant power.  2KW from gasoline is $600.

It seems the biggest inverters are intended to be powered directly from car battery terminals while running the car.  There isn't a cost effective way to power them from standalone batteries.  The vacuum would only be used for cleaning the car & the carbon monoxide fumes would help to loosen dirt.