It means " only one options" out of more they presumably have.
BUT: adverb
only, just, simply, merely: St Anton is but a snowball's throw away from Lech.
Collins Dictionary
On the other hand, being in the hands of big money might mean that she's controlled by big money, that is, wealthy people,
Pretty much this is what it means.
Although it might not mean wealthy people specifically but entities that have a lot of money to contribute to campaign funds or lobby. These could include political action committees of both individuals, corporations (in the US corporations are legally equivalent to people in a lot of situations), sets of individuals, and industry alliances (e.g. RIAA, MPAA, etc.)
Similar terms are "Big Business", "Big Oil", and a new one "Big Data" to mean the extreme power - political, financial or otherwise - wielded by the powerful members of a certain class.
Best Answer
This phrasing is often used in the conditional sense to indicate that if things go a certain way, then the path will be difficult. It's like saying “these difficulties will become your responsibility (or fall to you).”
In this specific instance, the message is essentially: