Income from a job is stable (relatively), income from other sources like say a monthly donation, is unstable.
So yes, my example is still accurate: they rely on the 1k/mo as STABLE funding.
Every penny of their income is important. If they had less content to provide to member stations, those stations would have less content and would pull in fewer donations. It then becomes a death spiral since less content results in fewer donations.
While federally originated dollars are a small portion of NPR's total income they're not unimportant since they can't be replaced by other sources. A 1% reduction in income means they need to reduce expenses by 1%.
In your analogy, $1k/month goes into savings. Losing that wouldn't break you financially. You're not spending your all of your income. If you were you'd need to cut your expenses by the $1k/month. In that case you'd consider that 1% pretty important.
More accurate would be saying I make a $100k/month of which $1k comes for a certain source, and then me saying that thousand is essential to my livelihood. I'd be lying if I said that; I make a whole lot less than $100k/month and I could easily forgo $1k/month today which just goes into my savings anyways.