Write the letter of recommendation yourself. Make an appointment to see him (no need to share you'll be bringing this along), and give him the sample letter to read - in your presence. Tell him you can only imagine how busy he is and you hope this will help inform and guide him on what to write.
You may remember that in high school you and your parents filled out lengthy brag sheets for your college recommendations. Chances are your guidance counselors composed your college rec letter by lifting straight from these brag sheets. This is sorta the same thing. Let the college adviser know that's why you thought to write the letter yourself. It's possible your college adviser may be procrastinating because he has so much on his plate and/or needs some more further information from you. That said, it's still pretty bad form on his part to drag this on and on.
If your advisor won't make the appointment to see you, or gives you a date that exceeds the date by which you need the letter, email him and send the rec letter you wrote as an attachment. Take the high road and apologize if you are imposing but you really, really need this letter from him by X date, and "please see the attached," in the hope it helps. Make the subject heading, "High Importance - Please Read." Let him know you are comfortable with him using sections of your letter. If you don't hear back, move on, as others here have suggested. Your adviser may be your biggest fan, but he's also a first-class weasel. It's time to cut him loose.
You could go to the dept chair and say you have now been placed in an untenable position and that you need this letter by a certain date. Offer them the letter and see what you can make happen without any blame. It's important you not miss out on an opportunity because of this adviser. Politely make that clear to the academic department and then move onward to someone else, or have them handle it.
Writing recs is part of a college adviser's job. A department chair may be able to attach his/her signature to the letter you wrote, or some version of it, and quickly give you what you need. There may be something tragic going on - serious illness, a divorce. Who knows. Either way, the department chair or staff should help. Best of luck!