I don't think storage for the captures carbon is really a limit. I think the main limit would be the materials to construct enough carbon capture facilities to do the job.
One nice thing about carbon capture is it doesn't matter much where you do it. The atmosphere does a great job of spreading CO2 nearly uniformly. You just need places with sufficient available energy and somewhere to put the carbon.
One possibility would be subtropical deserts. They have plenty of sunlight for energy and plenty of land that could be used without displacing many people.
Imagine carbon capture facilities that consist of a solar farm for power with the panels mounted a few meters off the ground, and we dump the captured carbon under the panels.
As calculated earlier, 1 gigaton of captured CO2 would give enough carbon to cover Texas to a depth of 0.017 cm. There are about 3000 gigatons of CO2 in the atmosphere, so if we captured all of it, that would cover Texas to a depth of 51 cm.
The 5 largest subtropical deserts have a combined area 22 times as big as Texas. If we covered just 10% of that area in solar farms to power carbon capture with a meter of room under the solar panels we'd have plenty of storage space.
At the efficiency of current solar farms and current carbon capture, they would be capturing about 10% more carbon per year than we are currently emitting. Cover 90% of those 5 deserts with such plants and in under a decade we could get back to preindustrial CO2 levels.
The big limit that I see on doing this is production of solar panels. At current production rates, covering 10% of the 5 largest subtropical deserts would use about 180 years worth of solar panels.
I have no idea if there are enough raw materials available to let us to increase that enough to make it worth considering.