The First Amendment does not explicitly mention campaign spending (or political campaigns at all), and until 2010, the First Amendment was not considered to apply to monetary spending in political campaigns.
The right to petition the government is explicitly protected, but that doesn't apply in the case of IL-9, which was an open race and therefore none of the candidates were actually elected representatives.
Even still, this is money on how a private entity decides who its going to support for a future election.
None of these people are even running for government yet.
If the democratic party wanted to so something about it, they could, but the freedom of expression and association guarantees that a party that wants to have lots of money spent on ads an such can do it
If Mongolia pays a bunch of US citizens to vote for some candidate that promises to push the US towards militarily supporting Mongolia, do you think the First Amendment supports that?
Or more accurately, imagine if the US had special rules and exceptions for dual citizens of Mongolia and the US that don't exist for any other country and then it allowed those dual citizens to push for certain candidates without having to be registered as a foreign lobby.
Now try substituting Mongolia with Russia or China.
The right to petition the government is explicitly protected, but that doesn't apply in the case of IL-9, which was an open race and therefore none of the candidates were actually elected representatives.