Macabra describes something dark, disturbing, or associated with death. It is the feminine form of macabro, agreeing with solución in the phrase "la solución macabra".
In the song, the phrase means "the macabre solution," creating an eerie contrast with the idea of solving a problem. Its dramatic, unusual sound and connection to death make it a memorable word to learn.
José Madero opens with a flat refusal: "No, ya no creo en Dios" [No, I don't believe in God anymore]. From there the song turns on everything around him. The city gets cursed ("Maldita ciudad" [damn city]), and every city is the same place wearing a new name: "Con diferentes nombres / Con las mismas calles" [with different names / with the same streets]. When someone offers to pray for him, he shrugs it off with "Nada cambiara" [nothing would change].
Then he bolts. "Me escapé por la ventana" [I escaped through the window] is a teenager's getaway, and the next line is almost funny: "Acá hace frío y olvidamos las chamarras" [it's cold out here and we forgot our jackets]. Chamarra is the Mexican word for a jacket. The fix he proposes is grim: "A convertir la nueva casa en fogata" [let's turn the new house into a bonfire], because "la vida es cara" [life is expensive] and the way out is "la solución macabra" [the gruesome solution]. He gets darker with "tal vez morir me salga más barato" [maybe dying will work out cheaper for me], where salir barato means to come out cheap. The ending softens into a plea to someone lying beside him: "Venga, quita esa cara" [come on, wipe that look off your face], an everyday Mexican way of telling someone to stop looking so gloomy, because "al fin y al cabo solo estamos de pasada" [after all, we're only passing through].