Whatever the draw is at 110v, you must multiply by 10X for the draw on the 12v battery bank. At a 1.4a/110v draw, for say 16hrs/day, that's 224Ah's per day, on a 12v system. Add to that another say 12Ah's/day for the inverter. A bank with a 20hr capacity rating of at least 472Ah would be needed, in order to maintain no less than a 50% soc, daily... and that would be very hard, long term, even on a set of true deep cycle batteries.
A daily charge to true full, will be necessary, in this case, but that 60w panel would likely not even float an already full battery bank of that size, even on a good day.
So no, the existing equipment would not get you thru a single day, let alone 3 or 4 days.