What is the global warming potential (GWP) of any gas over a 1 day time frame?
It can, but it's not very helpful. A large number of gasses (methane being one) decompose relatively quickly in the atmosphere to form other compounds. A longer time horizon means you capture all of that change in the metric (as compared to CO2), while if you did it for a day you'd end up with a figure that only really made sense for that day. The details of how it's calculated and why the time horizons are where they are is in the IPCC AR5 WG1 CH8 technical supplement (8.SM.11.1 Equations for the Global Warming Potential)