Are we required to obtain health care under the new Bill signed by Obama?

Answer 1

It will be required for most users:

"Most Americans would be required to have health insurance and face federal penalties if they do not buy it."

Source:
http://www.nytimes.com/2010/03/22/your-money/health-insurance/22consumer.html

http://www.whitehouse.gov/health-care-meeting/proposal (See the actual Bill, you'll see a section indicating the requirement for purchasing coverage).

Answer 2

http://www.cnn.com/2010/POLITICS/03/23/health.care.timeline/index.html

Also verifies that most Americans will be required to have insurance or pay a small fine.