It can, they just need to approach it not like a big corporation with a multi million dollar a year CEO but as a grassroots project.
If something like KDE can build a whole desktop on a shoestring budget with some donations, Firefox can too. And I'd gladly donate to it. Problem is I can't because you can only donate to the foundation. And I don't want to fund their dogood distractions, just firefox.
Besides, the search deal will end one way or another. Either Firefox will lose so much marketshare that Google no longer bothers, or the DoJ will finally ban the search deals. Relying on it is ultra stupid.