Not to pick on Political Animal, because the wonderful Digby is bad about this, too, but C'MON, MAN!
The Obama administration continues it’s progress on the Clemency Initiative.
The grammatical translation of that sentence is "The Obama administration continues it is progress on the Clemency Initiative."
"It's" is the only apostrophe s spelling that does NOT indicate possession. "It's" always - ALWAYS - means "it is."
To state the possessive of it, add s. No apostrophe.
"... continues its progress ..."