Is it still possible to get a decent job in academia (specifically physics) nowadays?
I've heard from a couple physics professors and chairs that it's somewhat difficult to find a first position in physics in general

This is a dramatic understatement. I always recommend reading the first chapter of Karen Kelsky's book. She demonstrates that our universities are not in crisis -- that was 20 years ago. Rather, they are in decay. Most departments are not growing; they are shrinking and cutting back. Yet, graduate programs keep pumping out PhDs.
For physics in particular: APS reports that in 2012, 1800 physics PhDs were awarded. In contrast, there are 9400 physics faculty positions total -- about half of which are at institutions with no physics graduate program (i.e., schools that -- with a few exceptions -- focus on teaching rather than research). From this, you can estimate what fraction of physics PhDs end up with faculty research + teaching positions (see also here).
In short: saying you want a faculty position is like you saying you want to join the NBA -- of course you do! But even for the best students, it is a long shot.

I'm concerned I'd be left out without a job if I tried to do so

Now for some good news. 1-year post-PhD, only 4% of physicists are unemployed. The overall unemployment rate for those with a physics PhD may be around 1-2%. There are research positions outside of universities, and there are also non-research positions that are both intellectually engaging and financially remunerative. Further, you should not have to incur debt to attend graduate school. Thus, attending graduate school in physics might be a good choice (financially and otherwise) even without the allure of a faculty position. But it is certainly good to be realistic about the situation; indeed, you might consider subfields, projects, and skills that could lead to interesting work both inside and outside of the university.
Note: this answer, and the statistics therein, refer entirely to the situation in the US.