I have never worked for the COE, but have bid on their projects. Did work for our state DNR as well as a HUD managed housing complex. Both cases required HUGE amounts of paperwork, proof of all insurance sent certified from my underwriter (no standard ins. certs accepted) and they MIGHT cut you a check some time during the next fiscal year. Unless you're set up to provide paperwork, performance bonds, etc. it is more of a hassle than it's worth.
And, unless you are the well capitalized folks like Davey or Azzplunge you're going to have to borrow operating capital if it is a project of any size. You make the call......