B. Each is nominated by his or her respective party
Explanation:
Part of the reason parties exist is to endorse a single candidate by the time elections draw near. There are primaries in which democrats or republicans can each vote for which of the available candidates in their party they want to face the chosen candidate of the opposing party.
The first stanza of the poem shows this explicitly where they say that there's an old lady on an island that has a daughter who lives on a different continent with an ocean in between. This is easily seen in the first four lines of the poem.