The cig lighter on most US cars has a 20A fuse. 20A*12V = 240 watts. You probably shouldn't exceed about 80% of rated, so the lighter socket may be only good for about 180 or 190 watts.

My home coffee pot shows a "nameplate" rating of 1,050 watts, so likelihood of successful use off the cig lighter socket would be quite low.

Most of the commonly available small inverters I've seen are in the 60W, 90W, 150W range. You'd likely need to look for a 1,500W inverter to handle my pot. Clipped direct to battery terminals, you could pull the (1500/12 = 125A rated, 1,050/12 = 88A needed) current safely - for a few minutes, but probably not long enough to brew coffee. Even with the engine running, most alternators are only rated at 35 or 40A on the small cars, (but up to 125A on some of the gas guzzlers). You might be able to run a large enough inverter, with the engine running, long enough to get coffee from a smaller pot - but don't shut the engine off before the battery is back up to starting level.

Multiply the volts by the amps, shown on the baseplate of your coffee maker. That gives you Watts. Your inverter should show how many watts it can put out. If the inverter output is less than what the pot needs, chances of successful operation are minimal.

You can get "warmers" with 50W or so ratings, AC or 12V dc - whichever you find, to heat a cup at a time - and use instant coffee (yeah, I know...).

John