Does anyone have any personal stories or links to share related to this? Will there be a research fund shortage within the next few years?
It's true that research funding varies by source and subject, but the bottom line is that funding is down across the board. The NIH and NSF budgets are have been shrinking (in real dollars) for a few years now, and funding for the big physics initiatives has been slashed. While there has been a slight bump in funding from sources like the DOE, the DOJ and DARPA, it doesn't even remotely make up for the declines in the other areas (and most researchers can't get that money, anyway).
I did my PhD at a major research school. As of late last year, they were quietly laying off staff (techs and staff scientists), reducing enrollment in the graduate programs, and increasing the teaching requirements of the remaining students (in order to offload their costs onto the university, away from grants). Moreover, the faculty are basically constantly writing grants, because the funding rate is so exceptionally low.
Now is not a good time to be in science.
Don't forget how much of this is driven by the president's budget office. Not surprisingly. this administration isn't interested in science.
Of course, the bit about this administration was extreme. But their funding priorities are less about basic science, relatively speaking.
That's not as true as you think it is.
It's important to know the source of the funding. Most schools (even reputable schools) make a guarantee that's tantamount to "we won't kick you out for lack of funding". Notably, that doesn't mean that you'll be funded to do research (hello, grading!), or even that they'll try to find you funding if you should happen to run out.
There are many ways to go wrong with this. The way that it usually works is that you're "guaranteed" funding for your first 2-3 years, and that money will come from a departmental slush fund for grad student training. After that, you've (hopefully) passed your exams and selected an advisor, and from then on, your funding is coming from his/her budget.
Woe to the fourth-year PhD student whose advisor loses funding! It can happen; I've seen it. Likewise, you're equally screwed if you happen to have a falling-out with your advisor after the departmental funding runs out. If you're viewed as a problem student, they won't necessarily kick you out, but they'll play a game of financial chicken with you, and I can pretty much guarantee that you won't win (I've seen this, too). It can also affect your ability to find a new advisor or collaborations; it's easy to become persona non grata when you're an under-funded grad student.
However, these are worst-case scenarios. Most commonly, you just get screwed by having to teach a lot more than you originally bargained. This is a terrible thing to do to a fifth- or sixth-year PhD student (who is also usually looking for jobs, writing a dissertation, publishing papers, etc.), but c'est la vie. You rarely see the blunt end of the funding stick until it's too late to do anything about it.
The best advice I can give about grad school: Know your adviser before accepting an offer. Non-tenured should be a big worry. No other students should be too. Use the beer night all schools feature to get honest assessments of potential advisers - after a few beers have set in. In a real sense, your adviser will be your venture partner with vast majority control even as you do the vast majority of the work. The decision of who to work with is therefore critical.
Expect this short-term clusterfuck to clear itself eventually sometime after November regardless of who wins.