Been playing that variation for quite a long time and always seemed to get a reasonable position while maintaining attacking possibilities as well. You forgot to mention the option of 3..e5, that is considered to be black's best reply. You should have a look at Karpov's games, he is known to have played 3.e4 with some success.
Help with Queen's Gambit Accepted

I play 3. e4 in the QGA, but I don't play this line, which I think is too slow to give Black any serious problems. I favour 4. d5 followed by 5. Qd4, developing the strongest piece on a central square and keep the other pieces elastic.

@ Mephisto and jMutzenbacher. Thank you.
Good point. 3...e5 is Black's best reply followed by 4.Nf3, but I doubt I will see it played at my current blitz rating. I've only seen the QGD once in my blitz games, even though it's by far more popular than the QGA.
Wow! As an experiment, I tried 3...e4 for the first time a few seconds ago. My opponent spent all of his move defending his precious c5 pawn while I continued with simple development. I never was able to capture his c5 pawn, so maybe I messed up somewhere, as the Queen's Gambit is not really a gambit. I prevailed with checkmate on move 18.

Ouch!!!
I was so focused on placing pressure on the c4 pawn while developing that I missed 11.QxRa4! Arg!! Arg!! Arg!!
Triple Arg does not say what I feel. Is there a better family friendly word?
I would be happy to play the Queen's Gambit Declined, but most of my opponents on chess live take the gambit pawn.
I just purchased an e-book from Everyman Chess where the authors recommend first playing what Nick de Firmian considers (Third-Move Alternatives for White) - 3.e4. What is the downside to playing 3.e4?
"With 2...dxc4 Black has given up the center and so White logically occupies it with 3.e4. It seems to us that any player who wants to master the QGA has to begin with the 3.e4 system, because it is White's most straightforward option and is currently considered to be fairly critical."
The diagram below shows both e3 and e4 played. Which pawn move do you prefer and why?