The Dems can't use the government funding bill to DIRECTLY obstruct a Supreme Court appointment. But they can absolutely use it to throw sand in the gears, by, say, passing a funding bill that the Senate can't really accept without further negotiation.

Dems run the House, there is absolutely nothing stopping them from making serious demands or even kicking a bill over to the Senate with provisions on oversight/elections/stimulus that will require a lot of additional work. You can be creative here.

Everyone has spent the last 18 hours saying "Wow, we should emulate McConnell and use all the levers at our disposal."

Guess what! A government funding bill is exactly one of those levers! And right now, Pelosi is planning on just doing nothing at all with it.

You can keep the Senate busy even longer by sending over impeachments. Bar has subverted the entire DOJ for political prosecutions, while Wolf is serving illegally as DHS head. They're central to Trump's designs on the election. Impeach both. https://twitter.com/emptywheel/status/1307395580587577349