You feel some sort of sense of duty to your job, you feel that you need to cover for your coworkers' shortcomings, you (want to) feel that your job "matters" so much that the company can't keep going without you. Reality check - If the company doesn't value a project enough to give you adequate resources to get it done, you should value it exactly as much as the company does - Not at all. It will get done when it gets done. Bonuses, you say? Yeah, they don't exist in the first place. I theoretically get an annual bonus - That depends 0% on my performance, and 100% on the performance of people entirely outside my department. The salesmen rule the world, simple as that. Hell, even my annual "performance" evaluation depends less than 25% on my actual performance. I could literally score a perfect "C" without getting a single one of my formal duties done.
Put bluntly, as long as upper management can get their email, your success or failure means nothing to the company on the short term. Yes, your project may well make the company more in the long run than even its core business - For which you will get zero thanks, because the C-levels have no clue what you do.
Make no mistake, I give my employer a fair day's work. But from what you've written, you would hate working with me, because I care about my job exactly as much as my boss, and his boss, and his boss' boss, all the way to the top of the food chain, do. If they make success possible, I will succeed. If they expect "Scotty the Miracle Worker" on a shoestring, you've already failed, don't waste your time fighting it..