Like DaveM says, melting ice is what keeps the inside cold. I find the current crop of 'Extreme' coolers do what they say, keep stuff cold for about 5 days. But you have to not open them much. This is why we have a two cooler solution. I use dry ice in the Extreme and that keeps stuff REALLY cold (basically everything inside is a solid ice cube). Twice a day I take stuff out of the dry ice cooler and put it in the other cooler, where it thaws for dinner. It then also acts like ice for the other stuff that can't be frozen (mostly milk, eggs, beer, etc.). We can do a 3 or 4 day trip this way without needing to restock ice. It's not perfect, but it works. The dry ice cooler almost never gets any water it in, since dry ice just sublimates into CO2 gas. In fact, water in a dry ice cooler will make the dry ice melt in no time, so it's got to be kept dry at can be.
One thing I should mention is that the Steel Belted coolers are made well enough IMO, but they are not as well insulated as the other stuff. Also ours is green (hey, it's traditional Coleman, right?) and that does not help. They make a white one (and a silver) and that's what I would go with now. But what it gives up in insulation it gains in tons of space inside and a better lid for more often opening. The Extreme cooler has a super snug top, but that's not great for getting Cokes and snacks out during the day. So it gets packed and not touched much.