Do 3 million people a year die from diarrhea?

Well, not really.
WHO has most recent statistics from 2004 and even they account for 1.8 million deaths.
http://www.who.int/mediacentre/factsheets/fs310/en/index.html

Lancet gives estimates 1.3 million deaths were caused by diarrhoea in 2008.
Global child deaths on decline.

Main cause of these death (beside lack of improved sanitation access) is rotavirus, killing about 500 000 people a year.
This is one of the ways Bill Gates is going to save so many lives. Investing in rotavirus vaccine is very cost-effective.
Currently largest organization supporting vaccination is GAVIalliance, which is working within 72 countries.

EDIT: Using this visible place I may add some comprehensive study of access to sanitation around the world.
Progress on sanitation and drinking water: update 2010. This is report about achieving MDG7.

Lancet has clear agenda in reporting their estimates.
Progress and barriers for the control of diarrhoeal disease
You can clearly see, by the terms they are using. They strongly propagate prevention and mitigation of diarrhoeal diseases. I doubt their estimate are undervalued.

Wait, so the problem has a solution at hand, and it's a matter of pumping cash into it, not hoping for a magical cure for cancer?

No, first population studies were performed primarily in South America.

There is no guarantee that other regions would have same results.

South Asia has more diversity in rotavirus genome. There is need for more scientific studies.

Secondly, there are few organization, who want to deploy new vaccines in the recipient countries. This isn't sexy thing to do.

There is particular problem with Somalia (and Western Sahara), which de facto don't have any health program and remain excluded.

Thirdly, lack of improved sanitation (mostly in South Asia) doesn't allow to decrease number of deaths to zero. Even with best vaccine coverage and mineral supplementation you can expect decrease in number of deaths by 300 000 a year.

Fourthly, chronic malnutrition (South Asia and Sub-Saharan Africa) is also responsible for part of these deaths, even taking into account vaccines and improved sanitation access.

Let's see, how amazing progress was made from grim XX century.

In the year 2000 over 900 000 children died of measles. In 2008 it was 160 000. In this year we can hope it would be below 100 000.

In the year 1990 there was 230 000 cases of polio. In the year 2000 it was 3500 cases. This year, AFAIK, there was 64 cases in India, 8 cases in Nigeria. Single cases in Uganda and different countries. I don't have data from Pakistan and Afghanistan, which could have outburst of polio. Apropos, there is currently vaccination intervention in number of Sub-Saharan countries. 72 million people are going to receive vaccine.

Oh, there is also "Reddit aspect". You would be paying some of largest international pharmaceutical companies hundreds million of dollar.