I think something like almost half of Americans are basically paycheck to paycheck and couldn't absorb a significant unplanned expense. I feel there is a lack of discipline in keeping a reserve fund, and managing your credit/debt so much so that a month's pay missing is putting folks into needing a food bank.
I recently had to absorb about $7k in unexpected auto repair expenses (risk of having two paid off vehicles with about 210,000 miles between them simultaneously need work). But I'd managed my affairs so that I could write a check for it (well two technically). I priced out personal loans to weigh using savings vs loan, and was offered $20k for 3 years around 6-7% (depending on up front fees) with my credit.
And I am a government worker (local) myself in my 30s with a wife (who I love but makes about 1/3rd of what I do) and a very soon to be teenager, two furry kids, a mortgage, etc. I am not some miser living on my own. Neither of us inherited any money or anything else like that either. Whenever something like that comes up, I immediately start working on way to replenish it, by working part time gigs, overtime (including voluntarily working Thanksgiving, Christmas and New Year's even if my shift is scheduled off), teaching for corporate clients, etc. Maybe some of the folks had drastic stuff come up recently and could not absorb another subsequent hit, but that should be a relatively small group.
Having said that, I'd be going absolutely ape shit about having to tap those reserves because I was being used as a political pawn in a partisan tug of war that is not damaging the players involved.
So I understand what they mean, but saying it that way is completely tone deaf, especially coming from a party not exactly known for being on the side of the average worker.