Q: What does "Drop and give me twenty, America' in 'Paul Ryan's song of himself' mean? The New Yorker magazine August 16 issue carries the article under the title 'Paul Ryan's song of himself' which is posted by Andy Borowitz. I as a non-native English language learner cannot tell whether this is Paul Ryan's own poem or simply a lampoon by the poster.
The 'Paul Ryan's Song' starts with:

"This morning I was at Equinox
  Getting ripped and shredded, pumped and jacked,
  Cross-training with Jeremy
  Who totally kicks my butt."

and wraps up with the following 4 lines:

"Because I am Paul Ryan.
    Paul Freakin' Ryan.
Drop and give me twenty, America:
    It's clobberrin time."

According to wordreference.com, 'Drop and give me twenty' is an imperative,
usually said to a soldier by a commanding officer: do twenty push-ups. (But it could be a joke if the speaker is not a commander and the person spoken to is not a soldier.) 
www.urbandictionary defines it "Heard, Understood, and acknowledged", commonly used in the US military, also used to show eagerness or joy. 
What does 'Drop and give me twenty, America' mean? 
Is 'Drop and give me twenty' usually used as an imperative as defined by wordreference, or just for affirmation of the order like 'understood, Roger' as defined by urbandictionary?

A: You're misreading the Urban Dictionary entry:  

HUAA  (13 up, 4 down)
      "Heard, Understood, And Acknowledged". Commonly used in the US military, dating back to the civil war to mean a command has been duly acknowledged. Also used to show eagerness or joy.
      "Drop and give me 20 pushups! HUAA?"
      "HUAA."

The entry is for "HUAA" not "drop and give me 20".  Incidentally, "HUAA" is pronounced as a word, "hoo-ah".  You might have seen military or ex-military characters in movies (like Al Pacino in "Scent of a Woman") go "hoo-ah!"
Your other source is correct.  "Drop and give me 20" is an imperative closely associated with the military, something your drill sergeant would say at boot camp, for instance.  Of course, most people don't use it as an actual command to do pushups.  It can be said as a joke but sometimes it isn't.  For example, "I can't believe you ate my pizza.  I should make you drop and give me 20!"
As J.R. pointed out in his comment below, the purpose of "drop and give me 20, America" in the song seems to be to tell America to get its act together.  
As for whether this is actually by Paul Ryan, I'm sorry to say American politicians in modern times have not been allowed to show that great a sense of humor.

A: "Drop and give me twenty" is a pop cultural reference from the movie "Animal House" (1978).
The poem you reference is written by humorist Andy Borowitz, who is most certainly not a Paul Ryan supporter.  Borowitz makes multiple references to popular culture, and particularly popular culture that is less popular in Manhattan than it is in the Midwest (and, obviously, Wisconsin), including various comic book heros, movies, and sports.  Overall, the writer's intent is to ridicule Ryan as a macho, overly-juvenile, simplistic man.  You may determine for yourself if you think his creation has achieved that goal.
Animal House has many "memorable quotes" that are in common use in America including the one you ask about here: "Drop and give me twenty":  http://www.imdb.com/title/tt0077975/quotes?qt=qt0479948 
The character speaking this quote, Doug Niedermeyer, heads the campus ROTC and is the main foil to the movie's heros.  He is a "square", militant, angry, and enjoys asserting his authority over others. "Drop and give me twenty" is a command for an inferior in his ROTC squadron to do twenty push-ups, and indirectly, a means by which the movie shows Niedermeyer flaunting his higher status and achieving satisfaction from it.
In the poem's context, this movie quote alludes to Ryan's penchant for pre-dawn workouts and the politically liberal magazine's perception of Ryan as a frat-boy / empathy-less militant. By drawing a connection between Niedermeyer, whom the audience does not like, and Ryan, Borowitz hopes to have the negative perceptions transfer to his political nemesis.
We will see much more writing of this nature over the next two months!
[BTW, the Niedermeyer character, and the above quote, re-appear in the 1984 teen rebellion anthem "We're Not Gonna Take It" by Twisted Sister, with Niedermeyer representing the unempathetic adult authority against which we all must struggle. Why, you may ask, do several large men dressed in awful drag, playing guitars far too loudly, perfectly express teenage angst? I probably had a good answer for you thirty years ago, but for right now I'm too busy enjoying the song :)
The quote is at 4:14 in this YouTube video: http://www.youtube.com/watch?v=4xmckWVPRaI ]
