The National Coalition for the Homeless website has a flyer (Publications->FactSheets) with the above title and they say that counting homeless people is difficult. Some people may be homeless for a short period and then find a home, while another family may lose theirs at the same time. Some stay with relatives, some live in parks, cars, and so forth. The Coalition also gives a national guestimate:

"The best approximation is from a study done by the National Law Center on Homelessness and Poverty which states that approximately 3.5 million people, 1.35 million of them children, are likely to experience homelessness in a given year (National Law Center on Homelessness and Poverty, 2004)."

They noted that the guestimate was based on service providers, and that not all homeless people used service (shelter) providers.

Homeless persons probably qualify for government assistance with medical care, but may not apply for it. My guess is that the guestimate is not included in the 40 million without health insurance, simply because they visited homes.

The Coalition also put out other flyers, including one on Healthcare and Homelessness (PDF).