I'm not a fan of the wine pump. It does very little (except create that pressure in the bottle) to protect a wine & actually removes the aroma esters from the wine. Whites do fine in the fridge for a week+. Reds don't last as long, but putting them in the fridge does slow down the oxidation without harming the wine. The obvious downside to putting wine in the fridge is one must remember to remove the bottle (of red) from the fridge long enough in advance to bring the wine back up towards drinking temperature.
The best solution to saving your open bottle of wine ...aside from not having anything left in the bottle...is to pour the wine into a smaller bottle where there will be less (or no) oxygen, which is what oxidizes the wine. If you can get your hands on a half bottle (375ml), once cleaned (dishwasher is fine) you can pour your leftover wine into that bottle, cork it & put it in the fridge.
I'll often do just that as soon as I open the bottle. I'll open a 750ml bottle, pour half of it into a 375ml bottle, put the cork in (so I remember which wine I poured in there) & put the half bottle in the fridge while enjoying the other half of the 750ml.
Again, if the amount you are pouring into the half bottle is more than 375ml, this solution won't work. And if it is less than 375ml, it will help (by lowering the amount of oxygen in the bottle), but won't work for more than a few days.
Stay tuned for more on what to do with leftover wine...