You can register and search available plans, as well as sign up via the Healthcare.gov website. It's being a bit glitchy for some people at the moment though - all the people who are checking it out. So you may want to wait a couple days for things to settle down. - https://www.healthcare.gov/
No way you can do it this week. It's likely you can't even do it this month. There are too many system failures, overloaded servers, and exchanges not ready to accept applications. How many of the 2.8 million people who logged in to healthcare.gov were able to actually get insurance? It's quite possible that none were able to, in your state.