yes

but it's nontrivial

whitewash curing (lime carbonatation) is the easiest process and the one most used in scuba, anesthesia, and hyperbaric chambers; though it's less energy efficient and involves higher temperatures than amine scrubbers, you can hopefully outsource that part of the process to something outside your house

the overall reaction is

cao + co₂ → caco₃

caco₃ is 44% co₂ by weight so each kg of co₂ you remove from the air consumes 1.27 kg of quicklime and creates 2.27 kg of chalk

with only water as a catalyst this typically takes about three months; without even water it takes about three years. as i understand it, with a few percent of lye as a catalyst it can be complete in under a second, which is how soda-lime cartridges for scuba rebreathers work

suppose your house is sealed except for 100 ℓ/s ventilation (212 cfm in medieval units). you're going to be exhaling into it, so maybe you want to reduce the co₂ content from 420 ppm (duude) to 250 ppm, 40%, so you run 40% of the air through a lime scrubber, 40 ℓ/s, which outputs effectively co₂-free air

this intake scrubber has to soak up 17 mℓ co₂ per second (420 ppmv of 40 ℓ/s); at 1 atm and 20°, pv/rt gives us 7.1 millimoles per second, which turns out to be 31 mg of co₂ per second, about 2.7 kg co₂ per day, consuming 3.4 kg per day of quicklime and producing 6.1 kg per day of chalk

if you're doing this without an alkali catalyst you probably need about 300–400 kg of slaked lime (whitewash or whatever) exposed to air. if we roughly estimate that as 200 ℓ at a 1-mm-thick paint layer it's 200 m² of freshly whitewashed walls. this will probably occupy a cubic meter or two in your house. soda-lime is probably a better option

either way you're left with about 190 kg per month of chalk waste (maybe with sodium carbonate in it) that you need to dispose of and replace with a bit over 100 kg per month of quicklime. you could conceivably handle this yourself by burning it in a lime kiln yourself a couple of times a year, but a more pragmatic approach might be to buy four 25-kg bags of quicklime every month (about US$150) or a one-tonne pallet every 10 months. a tonne of quicklime exposed to the atmosphere will probably absorb about a kg of co₂ per day even without water

you can reduce this a little by reducing the flow rate but pretty soon your own co₂ breath starts to build up in the space, especially if you're getting jiggy with your husband in bed

if instead of scrubbing your intake air you try to hermetically seal your house like a submarine you only need to remove 1 kg co₂ per day (per person) but you have some new problems

one is that by removing 1 kg of co₂ per day from the air you are effectively removing [edited] 0.73 kg of oxygen from the air per day, so your oxygen concentration will fall. when it falls by 50000 ppm (50 times through the filter) it starts to become a serious problem. you can do things to replace the oxygen but you can't detect this problem at all without oxygen sensors and it can cause you to fall asleep and never wake up

the other is that, with such a sealed life-support system, co₂ is far from the only gas you need to actively manage. water vapor, h₂s from farts, methane from belches, mercaptans from bad breath, and butyric acid from your gym socks all require attention. the life support systems on the iss are publicly documented and i recommend reading the reports to see how they deal with these issues

on the other hand you won't be breathing diesel smoke from the semis passing by and you'll be totally set if there's a poison gas attack

see also https://news.ycombinator.com/item?id=33579810 for the scale required to do this with a greenhouse instead of a lime scrubber, but if you garden you know that's also nontrivial