So Gary Allen has a really complete time line of the history of 911 in the USA. http://www.911dispatch.com/911/history/ here. I would recommend reading that. It's complete with correct resources and self sourced history.

Edit: his article answers your questions as well!

Historians mark the beginning of the American EMS system with the publication of Accidental Death and Disability: The Neglected Disease of Modern Society (National Academy of Sciences, National Research Council, 1966), generally referred to as "The White Paper". This paper concerned itself with "preventable" deaths, or deaths that had not to do with something like disease, but car accidents, work place accidents, essentially, deaths caused from human fault. The paper argued that many of these deaths were caused due to the time it took for patients to receive care (laying the foundation for pre-hospital care).

The idea of prehospital care and transport was not altogether new. In 1797, Dominique-Jean Larrey used a system of special carriages to transport soldiers away from battle fields. Bellevue Hospital, the first hospital in the United Sates, used horse drawn carriages as well as early as 1869. To give you an idea what these look like, Here is a picture of the horse drawn carriages used by Grady Hospital in Atlanta in 1896. However, it is important to realize hospitals during this time were very different than the modern day hospital. Hospitals would consist of large wards, and was really considered a place where people (the poor in particular) went to die. Funeral Homes often were the means of transport to the hospital well into the 20th century. Patients would actually ride in the back of the hearse.

After the release of the white paper, the National Highway Traffic Saftey Administrator (subset of the Department of Transportation) released its first curriculum for the training of Emergency Medical Technicians. When it became clear that space was needed to preform CPR, bandage wounds, carry patients on stretchers, the modern Ambulances soon followed. This took time to implement though, and use of funeral homes for transportation continued into the 70s in some places (particularly rural areas).

The second thing to realize is EMS has largely been influenced by US military interventions. The military originally showed the importance of pre hospital care for trauma, particularly in stabilizing patients prior to transport in a helicopter. The Vietnam war gave the data needed to prove this, and so great strides in treating trauma were made (in fact, recently, Iraq and Afganistan wars have dramatically changed trauma treatment as well, but that goes beyond the scope of this subreddit)

During the 70s, the Emergency Medical Services Act of 1973 dramatically improved development of regional EMS services, and the National Registry of Emergency Medical Technicians (the national board which certifies people to this day) was formed in 1970 to standardize practices. Much of the funding was lost however, after Health Care became managed by Block Grants under Reagan, a system which did not favor EMS funding. The ideas and practices of what EMS needed to accomplish, and what qualified as proper care began to evolve in the 90s, and by that point EMS was an integrated member of the emergency response trifecta (Police, Fire, EMS).

A highly recommend you peruse emsmuseum.org, which has lots of excellent information on the people behind getting EMS started in the united states. For more information on modern day EMS, please visit us in /r/EMS.

Source: Advance EMT: A Clinical Reasoning Approach, Melissa Alexander and Richard Belle

In 1968, a solution was agreed upon. AT&T chose to implement the concept, but with its unique emergency number, 9-1-1, which was brief, easy to remember, dialed easily, and worked well with the phone systems in place at the time. http://en.wikipedia.org/wiki/9-1-1

Follow-up question: how come US and Europe managed to diverge on this thing too (911 vs 112)? Wikipedia is bit short on the history of 112, but gives us following:

The CEPT recommended the use of 112 in 1972

and

In 1968, a solution was agreed upon. AT&T chose to implement the concept, but with its unique emergency number, 9-1-1, [..]