To me, like someone said, this is nothing but a riddle.
In California and New York,
Democratic challengers
will need to spend more heavily in the months ahead to beat back rivals for their own party’s nomination,
or [they will need] to introduce themselves to voters against Republicans who are already well-known.
It seems like too much is missing to make these statements parallel. The comma though strongly indicates this split.
In California and New York,
Democratic challengers will need to spend more heavily in the months ahead
to beat back rivals for their own party’s nomination,
or to introduce themselves to voters against Republicans who are already well-known.
However, the meaning here doesnt get to me. The goal for the challengers is to win the election process within their own party. This can be achieved either "by beating back rivals" or by "introducing themselves to voters in debates against well-know Republicans". But... isn't this introduction of themselves just one of many measure they can take to achieve their goal of winning their own party's nomination?
So on a meaning level, this choice is not parallel. Either we achieve the goal A or we take one specific measure that could lead us to achieve our goal A. What?