My understanding is that the syndcate would be committing an act of extortion.
Under the RICO Act, IF the politician conspired with the syndcate or had something like an 'understanding' with the syndcate then they (any and all involved) could also be charged with the crime (extortion), racketeering and conspiracy.
Additional crimes/laws to consider:
- Campaign finance violations
- Money laundering
- Compelled speech (1st Amendment)