The Decemberists – One Engine lyrics

Actually, to correct the above post, a martyr is (according to Merriam Webster):
- a person who is killed or who suffers greatly for a religion, cause, etc.
- a person who pretends to suffer or who exaggerates suffering in order to get praise or sympathy
- a person who suffers greatly from something (such as an illness)

In the "Hunger Games", all the tributes are martyrs to the Capitol, but perhaps particularly Katniss, who martyrs herself for her sister.

The song is sung from the perspective of one or two sympathetic observers in the know: haymitch abernathy and/or cinna. It is written in the present tense (makes, is, are breaking), thus told while the hunger games are being televised. Neither cinna nor haymitch can say out loud what they're thinking so they is speaking to us (pseudo-dstrict watchers) in a symbolic language.
The hunger games are imagined here as a race of kids made into killing machines ("engines"): the first "engine" to roll over the winning "line" equals the last kid alive. By "barely making it away", an "engine" in a normal race is doomed to lose, but in the context of the hunger games, "barely making it away" means one "engine" refuses to go along with the killing race. Losing physically means winning morally!
Notice how the line "one engine barely makes it away" is repeated twice (once each for peeta and katniss). While it could be observed as an act of resistance by the capitol viewers, it is an act of liberation of the districts ("hold on, they're breaking their bonds"). The third time the line one "engine barely makes it away" is used, it signifies a united katniss-peeta team.
A "martyr" is someone who makes a great sacrifice or even dies for his moral principles or religion. Haymitch's (and maybe also cinna's) survival plan for his two mentorees is their purported martyrdom out of love for one another. He hopes to appeal to the emotionally gullible capitol residents. But even without his plan, both katniss and peeta are willing to die for a greater cause anyway: katniss for prim's survival and peeta for his dignity as a human being.
In the second stanza, the word "line" is brilliantly used as a motif: a "martyr line" can be read as empty talk by the capitol to cast brutal killing and dying for one's district as a so-called honor of martyrdom for one's peers. Alternately, it can be read as referring to the alleged "line" of "victory" in a car race: by refusing to be the last survivor, the "martyr" deliberately does not cross this alleged "line" and therefore will die for his or her belief. Either way, being a forced or voluntary martyr is a "bitter pill to swallow", especially for a teenager with only a budding set of personal ethics.
The "line of right" can also be read in two ways: first, as the "line of right and wrong", which is being crossed cruelly by the capitol and numbly accepted by the districts after decades of brainwashing. "it will barely make you [as a district viewer] feel" anything, neither proud of your tribute's moral victory nor sad for the tribute's death, because you have been forced to confuse right and wrong. Second, the "line of right behavior" - resistance - will lead straight to the resisting tribute's death, barely allowing time to feel pain or fear.
Haymitch curses the capitol viewers with concealed wrath: "i'd like to get you in some kind of […] trouble", but rapidly switches to sending support to his embattled mentorees: "bear down, they'll run you aground! " the suffering shall no longer be borne by the child tributes alone: "we all must suffer awhile in a way. " the repeated use of the word "way" reveals haymitch's helplessness in constructing a plan of revenge: "some kind of way" is too unclear, undecided, open-ended to function as a successful plan.
Excellent ending to the song: one "engine makes it a*w*a*y" - that's the only "way" to do it! But the "engine" is repeated three times: not only katniss and peeta survived these hunger games, but also the humanity and dignity of some of the others, especially prim and even thresh and foxface.

I think it's a very good song for the hunger games; it's very fitting. "martyr" is someone who changes their religion, belief, lifestyle, or something of the sort. The "martyr line" refers to succumbing to the capitol, in my opinion. Over and over again the lyrics refrence to the capitol; about how they'll "run you aground", and about "i'd like to get you in trouble in some kind of way" is about the capitol attempting to crush katniss (and peeta, maybe?), yes? Anyways, very nice song.