There are about 800,000 doctors in the US (http://www.census.gov/compendia/statab/ranks/rank18.html); lets conservatively estimate 5 times that many other medical workers providing patient services (e.g., nurses, PA's, medical office assistants).
All these people need to be trained on the new system, except the ones who are replaced by it (1). Every hospital and doctor's office in America need to modify their business practices to fit the new electronic system, and more than 300 million sets of medical records need to be entered into the new system.
(There are about 300 million people with medical records, many of whom have seen multiple doctors.)
The new system also needs to correctly deal with most aspects of medicine, and be flexible enough that unforeseen circumstances can still be tracked.
I don't think $100 billion is unreasonable.
(1) [edit] amusing question: Obama talks about "212,000 new jobs created". I wonder how that compares to the jobs which will be "stolen" by the new technology he proposes? I'm all in favor of creative destruction, I just find the language amusing.
Rather than getting your fuzzy estimate by dividing, use a more accurate website to see there were 633,000 doctors in the US in 2006 (http://www.bls.gov/oco/ocos074.htm).
The rhetoric of the Obama stimulus is to create state jobs now that will somehow make the US economy more efficient later and then decreasing state jobs when economy is in better shape and letting private sector take over. I am not saying that is what will happen, mind you.
100 billion / (6 * 800,000) = 20,000 per person. Let's say 25% of that is HW and software that gives 15,000 in training per person. Just how hard to they expect this stuff to be?
I imagine it will be equivalent of 1-2 semesters of college courses ($3-5,000). It's not like we can just throw a highly discoverable UI at them and hope most nurses can figure it out.
The medical office assistant now needs to understand the whole system well enough to figure out which external records are mine (and not those of another guy with the same name as me living in Buffalo). That's trickier than figuring out ebay.
It might be a bit short of $15k/person, but its not too far off.
There are deployment costs. Existing business practices will need to be changed. The transition will need to be seamless, or else treatment orders get lost. Add in the costs of it being a government operation, and you get a number on the order of $100 billion.
Maybe $50 billion is a better number than $100 billion, but $1 billion is probably far short of what it should be.