That is not the same situation. With a politician, one source can contribute X, and another source can contribute Y, and both of their contributions influence the politician. In other words, if the politician loses a source of donations equal to 90% of his or her donations, there is probably nothing that would replace that donation. The only supply is percentage of the politician's time so to speak, which might effect how much someone is willing to donate in the absence of another donation, but probably not in the way the politician would like.
With Mozilla, the supply is one item, the default search engine for the search bar, something which has high demand. That means if Google were to become less interested in paying for the search bar, Bing would be waiting at the gates to do so. They could lose money if that were to happen, given that Google was the highest bidder, but that in no way makes them beholden to Google.
Not sure what you mean by high demand, it has certainly has had strategic value, but the grand total of companies that would be interested in the search box are Google, Microsoft and Yahoo.
I wouldn't be looking forward to the next set of negotiations if I had Microsoft and Yahoo as my fallback positions.
With Mozilla, the supply is one item, the default search engine for the search bar, something which has high demand. That means if Google were to become less interested in paying for the search bar, Bing would be waiting at the gates to do so. They could lose money if that were to happen, given that Google was the highest bidder, but that in no way makes them beholden to Google.