You have at least 10 times the likelihood of suffering a severe life changing reaction or death from the DTaP vaccine than you do being hospitalized for all 3 of the diseases in the DTaP vaccine, combined.
Your chances of actually getting Diphtheria, Tetanus, or Pertussis are 1 in 256,145 and a less than 1 in 1,000,000 chance of having a serious case where you require hospitalization or suffer death.
Diphtheria typically causes a sore throat, fever, swollen glands and weakness. In the most severe of cases, diphtheria causes a gray material to coat the back of the throat causing a person to struggle to breathe. The last reported case of diphtheria recorded in the US was in 2003, so you have a 0% chance of catching it.
The US reported 4,887 cases of diphtheria between 2011-2014 outside the US. The chance of actually having a serious lasting health problem or facing death from diphtheria itself is less than 3%. Meaning, less than 146 people have become seriously ill or died from the disease between 2011 and 2014 in the entire world. 
Tetanus is a bacterium that infects the body through a break in the skin. Once Tetanus is in the body it spreads through the body into the muscle tissue. It affects the muscles tightening them up including the jaw (formerly known as lock jaw). Patients usually fully recover with long term antibiotics (usually 3-4 weeks).
The US reported 233 cases of tetanus 2001 to 2014. 176 of those cases were intravenous drug users (so if your not an IV drug user the chances are basically 0% that you would contract tetanus in the US). Only 26 suffered serious effects or death, and it is unknown if the virus caused these effects, or if it was the drug use because all of those who suffered serious effects or death were the drug users.
Pertussis is similar to the common cold. Most common symptoms are runny nose, sneezing, low-grade fever, and a mild cough. Less than 13% report more severe symptoms such as excessive phlegm, or difficulty breathing. Infants are more likely to suffer serous complications like pneumonia because of their inability to communicate.
What are the actual chances of getting Pertussis? There have been 25,827 reported cases in the entire world from 2004-2014 (1,012 from the US). Of those cases, 100 have had serious side effects or died, and 76 of them were under 1 month of age. Yet, the Pertussis vaccine isn’t given until the 2nd month of life, because they are proven ‘unsafe’ for anyone younger than that.
The CDC, the US government, and the world health organization, the ones recommending that you and your family get vaccinated, are the ones stating the above facts.
Know the risks
The chances of having a mild reaction to the DTaP vaccination are 1 in 3-4. (Crying for more than 4 hours, vomiting, swelling to the arm or leg, fever over 101). The chances of having a moderate reaction are 1 in 6,000 (requiring a hospital stay). The risk of having a severe reaction and or death is about 1 in 100,000. These statistics are from just 1 dose of the vaccine. The CDC recommends 5-6 doses before you are 18 years old. With each dose of the DTaP vaccine given over time, the risk of side effects increases.
The DTaP vaccine series is given with other vaccines. This presents additional dangers as all testing and side effects reports are specifically relevant to a single dose. The safety or side effect of the DTaP vaccine given in conjunction with other vaccines has not been tested so the statistics are irrelevant in those cases.
You can learn more about the vaccine injury program by calling 1-800-338-2382 or visiting the VICP Website.
References & Additional Resources: Diphtheria, Tetanus, and Pertussis (DTaP) – Vaccine Information Statement, Pertussis Fact Sheet, Diphtheria Clinicians, Vaccine Side Effects