Liquid??!!!!!!
1) if there were liquid present close under the ice, the surface would deform and flow, but it doesn't
2) Even though the water ice is "warm", this is wrt solid CO2 at 147 K. It only gets 10 K or so warmer than that.
3) Given the thermal conductivity of water ice, you won't even hit a brine melt temperature for several km
4) The pressure effect on ice melting (ice 1h crystal structure) is only worth 25 K, max, and that requires 4 K bar of pressure (105 km burial on Mars)
In short, you're talking out of the back of your trousers again.