Those are the three branches of the U.S. government, but in this context, they mean the three institutions required to pass legislation; a bill must go through both the House and the Senate and then be signed by the President to become a law. If Democrats had taken one of those institutions, they could have slowed the Republicans' agenda..
Yup. Call your Senators and tell them you have no faith in the party leadership, and that Chuck Shcumer cannot continue as Senate Minority Leader. If they're up for reelection in the next two years, tell them you're happy to support a primary challenger if it's the only way to get change.