The White House firmly restricts items that visitors can bring with them during their tour, including cameras, handbags, bookbags, food/drink and strollers. If it's not convenient for you to store your bags at your hotel or in your car, here are some suggestions:
If your tour is earlier than 10 a.m., you can go to Union Station on Metro, where a baggage storage facility is available near Gate A from 6 a.m. to 10 p.m. daily. A photo ID is required. Cash and credit cards are the only accepted forms of payment. Rates are $3-$6 per hour, ($11 for more than 3 bags) depending on the size of the bag. For more information on Union Station's baggage storage facility, please call (202) 898-1592.
You can designate one member of your group to wait with your bags while the rest of your group takes the self-guided tour. There should be ample time for that group member to tour as well.