Here's a short video on how mail is handled for the President which Robyn posted on mecfsforums.com:
http://www.whitehouse.gov/blog/Letters-to-the-President/
Here's the transcript of the video. The President gets over 100,000 letters/e-mails/faxes/phone calls from the public per day and gets to read 10 of them per day. It looks to me like chances are higher if you send a paper letter, include your address (since he handwrites letters back), and include a picture or something.
0:04 (birds chirping)
0:09 The President: These letters, I think, do more to keep me in touch with what's
0:14 happening around the country than just about anything else.
0:16 (birds chirping)
0:21 Some of them are funny, some of them are angry,
0:24 a lot of them are sad or frustrated about their current situation.
0:32 Mr. Kelleher:
In his first week as President, he asked for ten letters every
0:37 day and every day since, we've given it to him.
0:42 (music playing)
0:49
We get 65,000 paper letters every week,
0:54 we get something like 100,000 e-mails, 1,000 faxes,
0:58 2,500 to 3,500 calls per day.
1:02 And our job is to take all that information in, to do it --
1:07 the best analysis we can about what we're hearing from the
1:09 public and respond individually to all those folks so they know
1:12 that the President is listening.
1:13 (music playing)
1:23 Anyone that sends a message to us, it comes into our offices,
1:29 our staff sorts through them,
they identify those that meet
1:32 our three tests: Are they something that's representative
1:35 of the mail that's coming in, is it representative of something
1:37 in the news, and is it something that's a compelling message?
1:40 They pile that mail together; some of it ends up here on my desk.
1:43 (music playing)
1:45 I sort through it, categorize it by issue,
1:48 and then every day I go through them and pick the ten that best
1:52 represent what's happening right now.
1:56 It's a good dialogue -- a direct relationship between
1:59 constituents who have these concerns and the President who
2:02 desperately wants to get those messages.
2:05 The President's talked about being in a bubble,
2:06 and our job is to make sure that he gets out of it every day.
2:09 (music playing)
2:15 Hey, Joni.
2:16 >> Hey, Mike.
2:17 Mr. Kelleher: How you doing?
2:18 >> Great, how're you doing?
2:19 Mr. Kelleher: Good.
2:20 How's everybody doing?
2:21 >> Thank you.
2:22 Everyone's doing well.
2:23 (music playing)
2:26 >> Hey, Katie.
2:27 Ms. Johnson: Thank you.
2:28 So this is for tomorrow?
2:29 >> Yep.
2:30 Ms. Johnson: Okay.
2:31 >> Is that good?
2:32 Ms. Johnson: Yep.
2:33 I'll give it to him.
2:34
He probably replies to somewhere between three and four a night,
2:36 so over the course of the week, you're writing 15 to 20 letters.
2:39 So he writes a lot.
2:40 And he hand writes every single one of them.
2:42 Some are longer, some are shorter,
2:44 and the issues totally vary.
2:45 (music playing)
2:52 The President: Lately, I've been getting a lot of health care letters and this
2:54 is a good example.
2:56 "Dear Mr. Obama, my son-in-law, age 42,
2:59 had a heart valve replaced two years ago.
3:02 His wife and two children pay $1,200 per month for health insurance.
3:06 They cannot get another provider because he has a pre-existing condition.
3:13 He's now unemployed, so my husband and myself are helping them.
3:16 We're in our mid-60s and this is draining our retirement."
3:21 There's so many letters like that that I'm receiving every day.
3:26 You know, here's another one.
3:28 A woman whose husband retired from AT&T at 61 is waiting to
3:33 get on Medicare.
3:35 You now have the company in negotiations with the union and
3:39 may decide to stop health care for retirees.
3:45 Got another one, an antique business in Alabama,
3:49 they are on the verge of losing their business because they just
3:54 can't afford to pay the premiums --
3:57 their premiums increased $70 per month just this month.
4:02 So a lot of the stories are heartbreaking.
4:07 People who work hard -- a lot of times they'll say,
4:10 "I've never written to a President before,
4:12 I'm not looking for a handout, all I want is just a fair shake in."
4:17 And it ends up being a powerful motivator for me when we try to
4:21 move this health agenda forward.
4:25 Now, some of them are more cheerful and, you know,
4:28 this one for example.
4:30 "With all the huge money difficulties facing our country,
4:32 I thought you might like to see how someone spent their $250
4:37 stimulus money.
4:39 Thank you for all the pleasures from tending my raised bed and
4:42 from the vegetables I hope to enjoy."
4:44 So she set up a vegetable garden and she sent me a picture.
4:51 There's a beautiful letter that I got just a couple of days ago
4:53 I'm going to be responding -- from a woman who had found a
4:58 letter and she's forwarded it to me,
5:03 a letter from her father when he was fighting in World War II.
5:08 She had just been born and he had just gotten news of her
5:11 birth and he sent this letter, "My Dearest Daughter..."
5:15 And explained what he was doing in Europe during World War II
5:21 and why this was so important and what the country meant to
5:24 him and that someday she'd be old enough to read it and
5:27 understand why this was so important.
5:30 You know, you get letters like that and it --
5:32 it gives you a sense of what's best about America and inspires
5:36 you, and makes you want to work that much harder to make sure
5:39 that that -- that spirit is reflected in our government.