A truck heads toward the White House from within the city, then, presuming that no one really has any business near the White House because no one can really get in unless they are military personnel, the streets would likely be mostly clear, giving the trucks more than enough space and time to get up to at least 60+ MPH. How do you stop three semi-trucks going 60MPH heading straight for you, regardless of whether you think it's suspicious or not.
Adding to that, your average attack helicopter takes 30+ minutes to fuel up, start up, and take off. If the trucks only ran one checkpoint, then why the forget would the chopper have been in the air 30 minutes before hand. It's not like the frontlines are that close to the capital that you can send in chopper support from that loving distance.