Bacterial growth in standing water in a coffee maker?

I use a Keurig coffee maker – the kind that has a water tank that holds 1.5 liters (approx.). When it makes a cup of coffee, it then draws in another 6–8 ounces from the water tank into the heating tank so that it always has boiling water ready for coffee.

Based on my coffee consumption, I have to fill the 1.5 liter tank every couple of days. So there is always water in the tank; sometimes it has been sitting there for 2–3 days before it empties and I have to refill the tank.

What, if any, risk is there of bacterial contamination in that tank on the 2nd or 3rd day? (yes, the tank has a plastic cover, but the tank has some openings at the top and bacterial are very small). Am I better off running a thin water line from my kitchen faucet to the bank of the Keurig and only filling it enough to make today’s coffee?

Or am I overthinking this?