No that's not how the House of Representatives works.
Every single representative gets to choose on their own, on behalf of their constituents, how to vote. That is so important for us holding our representatives accountable for their actions.
The House doesn't operate by party. That would get in the way of representatives' jobs of representing us.
So no, it's not up to Republicans to figure out what the chamber is going to do. It's up to all of the representatives, regardless of party, to figure out what they're going to do, and so far Democrats have been voting unanimously that they would rather keep the chamber from moving forward.
The sad thing is that many Democrats have been overtly saying that they are voting this way for partisan reasons. Shutting down the House for partisan reasons.
I hope their constituencies appreciate their choice.