According to the CDC, "Ticks can attach to any part of the human body but are often found in hard-to-see areas such as the groin, armpits, and scalp. In most cases, the tick must be attached for 36 to 48 hours or more before the Lyme disease bacterium can be transmitted." They also go on to say that if a tick is attached to the skin for less than 24 hours, it is unlikely to transmit Lyme disease. .
The phrase to be highlighted here is "IN MOST CASES." The time to transmit the Lyme spirochete will vary greatly depending on many factors, especially the life stage of the tick. The most populous form of Ixodes tick to attack humans is the nymph form which is very tiny (less than 2mm) and very hard to see. The nymph form is the most dangerous form to man because it is so very small and can be overlooked for days, and the transmission time for nymphal ticks is less than for adults.
A study from the Institut Pasteur has shown that nymphal ticks can transmit Lyme disease in less than 12 hours.
"All the European species of B. burgdorferi that we studied were detected in the salivary glands of adult ticks before a blood meal, suggesting the possibility of rapid transmission of the bacteria following a bite.
The results were consistent with this theory: infection occurred within 24 hours of a bite from an adult tick. Moreover, our analysis shows that nymphs infected by European species of B. burgdorferi are capable of transmitting these pathogens within 12 hours of attachment.
Our study proves that B. burgdorferi can be transmitted more quickly than stated in the literature. It is therefore vital to remove ticks as soon as possible after being bitten to prevent infection." 
Another study has demonstrated that accelerated transmission of Lyme disease spirochetes can occur if a tick is only partially fed and then attaches to a second victim. 
The take home message is that Lyme disease can be passed to a human through a tick bite much faster than the literature and the CDC indicate. Don't assume you're immune. You can get Lyme disease more than once! Take preventative measures. Nymphal ticks are prevalent in spring and summer. The best way to prevent Lyme disease is to avoid areas where ticks live, especially wooded, bushy areas with long grass. You can decrease your risk of getting Lyme disease with some simple precautions: wearing light colored clothing with long sleeves and pant legs, using insect repellents on skin and clothing, and checking your clothing, yourself, your children and your pets for ticks. Remove a tick as soon as possible with tweezers. Look for more detailed information on prevention in the next post.