Most contamination from eggs (primarily salmonella bacteria) tends to be found on the shell. If you immerse the shell in boiling/simmering water, you will kill anything on the surface. In the vast majority of cases, your egg should be safe even from a brief bath in hot water.
However, if a chicken is infected with salmonella, the bacteria may also be found in the interior of an egg. Multiple food safety sources indicate that this happens in about 1 out of 20,000 eggs. I don't know how reliable that number is, but it comes up on a number of official food safety sites. With that incidence, safety information sources estimate that an average person will encounter such an egg once in 84 years or so.
(Note that the vast majority of salmonella illnesses are not caused by these "internally infected" eggs: most contamination comes bacteria on the shells, which then either gets mixed with the eggs through poor breakage or with other foods that come in contact with them.)
If you do not thoroughly cook the interior (as in soft or medium boiled eggs), you won't always kill the bacteria found in the interior of an egg. That's why many food safety organizations actually recommend that you always cook your eggs thoroughly -- not runny sunny-side up eggs or soft-boiled eggs, for example.
Since you're clearly willing to eat these eggs in any case, you're already taking that 1 in 20,000 risk (or whatever). The question is whether the short time spent cooking will make it significantly more likely that the salmonella will multiply and become more likely to cause illness.
As long as the eggs are cooled immediately (say, immersed in cold water) and then refrigerated promptly, the risk should still stay pretty low. In fact, it should probably be as safe or safer than the situation with most Europeans who would eat a runny egg, since they tend to buy and store eggs at room temperature (but only for a day or two). You may even be safer eating an old soft-boiled egg than a fresh runny omelet, since there's less opportunity for the egg to get in touch with an infected shell than with an omelet.
Basically, if you happen to encounter one of those 1 in 20,000 infected eggs, you have a chance of getting sick whether you eat it raw, in a runny omelet or sunny-side up, or soft boiled. Obviously, the faster you tend to consume that egg in a not-thoroughly-cooked state, the better your chances that the salmonella concentration won't be high. In the end, if you're eating soft boiled eggs in the first place, you have a very small chance of getting sick anyway. Waiting a day or so after boiling (as long as the eggs are kept refrigerated and cooled quickly after cooking) is not going to significantly increase your chances of getting sick. But the longer that egg is out of the chicken in general, the higher the risk.
If you're afraid of the 1 in 20,000 risk, the only good solution is to buy pasteurized eggs. However, they sometimes have an inferior taste. (Basically, salmonella can be killed at a temperature lower than the temperature where egg whites thicken -- around 145F, but it requires precise timing, temperature, and other conditions.)
In that case, I wouldn't hesitate to soft boil the eggs, chill, and store for a couple days. But do you want to eat a cold soft-boiled egg anyway? If not, just eat them fresh.
