The Tapwrm+SacCon engine is fairly common right now.
Here are my thoughts about how to respond to this. Note, I do not claim to be a strong player, so please offer better ideas and critique.
1) Manage my credit level so the drip is not a problem. This feels tricky to do since staying below 10 credits as Corp leaves you with few options. So, this probably is not a good option.
2) Purge aggressively. To do this, you need to be able to give the Runner free turns. If you have passive econ drip and a decent set of ice -- or great faith in your R&D -- then you might be able to do this. Feels like a better option for a glacier-style deck.
3) Ignore it. This works if you do not care about the Runner being really rich. I could imagine some Jinteki net damage decks falling into this category if the Runner does not have Feedback Filter, but this seems like a super risky strategy.
4) Slot tech. Obviously, you can't wait until the game to do this. You can put in anti-virus tech such as CVS and Macrophage or target the SacCons with Best Defense. I suspect the anti-virus tech will have wider utility both right now and in the future, but I could be wrong about that.
I'd be interested in other thoughts.