I don't like Schumer, or anyone in Democratic leadership, honestly, but I want people to think through how a government shutdown would go. A shutdown would almost immediately be felt by many people, as services stop, federal buildings and parks close, and people stop getting paid. These are all things people don't like, and they are also all things the Trump Admin are trying to do, despite being deeply unpopular.
A government shutdown right now because the Democrats blocked a spending bill would be met with wall to wall coverage in the corporate media about the Democrats blocking the bill. The Trump Admin and the right-wing media would then have carte blanche to blame the Democrats for everything bad about the economy that's coming down the pipe due to Trump's disastrous policies. Unemployment? Closed offices? National Parks closed? Checks not coming in? The Democrats did that!
Right now, Trump and the right-wing media don't have a leg to stand on when they try to blame anyone but themselves. A government shutdown right now would give their lies plausibility that currently does not exist, and it would be unlikely to extract any concessions from Republicans on this bill anyway, because many of them want the government to shut down, in some cases permanently.