These state and local governments must balance their budget (unlike the federal government), and the shortfall in funding due to the pandemic is hitting them hard. It means their will be drastic budget cuts for those governments, resulting in massive lay-offs (which will just make the economic problems of this country worse, and will drastically affect the level of service they can survive).
Democrats want to help these state and local governments. Republicans do not. They seem to be afraid that some of the aid will go to Democratically-controlled states -- and they don't want to help anyone that won't vote for them (or pay them off in some way).
Here's how part of how Paul Waldman (The Washington Post) describes the political games Republicans play instead of helping those hurt by the pandemic:
The challenge states and localities face is simple: The pandemic has increased the demands on their services at the same time that the economic downturn reduced their revenues. Since in most cases they’re required by law to balance their budgets, they have no choice but to impose draconian cuts — often in the form of layoffs — at the worst possible time.
At some point, Republicans decided that this is only a problem faced by places where lots of Democrats live, and they’d be damned if they’d help those places. They came up with the term “blue state bailout” to describe what they couldn’t possibly agree to.
Of course, the crisis has affected state and local budgets in Republican and Democratic areas alike, and the funding would be allocated according to factors including population and the depth of the recession in different states. The HEROES Act, which Democrats passed through the House in May, would have provided $206 billion in funding to states won by Trump in 2016 and $208 billion to states won by Hillary Clinton.
But the fact that they’re simply lying about who benefits isn’t the worst thing they’re doing. What’s far more repugnant is the principle that underlies their position, even if they were telling the truth: If Americans need help, we should first determine what party most of them belong to, then provide or withhold that help accordingly.
Whatever else you might disagree with Democrats about, this is simply not something they do. They don’t say “We should extend Medicaid to poor Americans only in blue states,” or “Alabama has some of the lowest-performing students, but since the state votes Republican they shouldn’t get education aid.” Republicans are the only ones who think this way. . . .
In the worst national crisis of our lifetimes, once again, Republicans have shown us who they are.