This debate hinges on the fact that impeachment is a two step process with the final step relying on republicans in the senate to do the right thing. You know what house democrats can do without needing senate republicans to do the right thing?
Hold trump admin officials in contempt and throw them in jail. This power has been upheld by the supreme court over and over again. In 2007, "The Congressional Research Service issued a report in July that confirmed Congress's inherent contempt powers. It explained how they work: "The individual is brought before the House or Senate by the sergeant at arms, tried at the bar of the body, and can be imprisoned in the Capitol jail.""
In 1821, the supreme court reasoned that without this power, congress would "be exposed to every indignity and interruption, that rudeness, caprice, or even conspiracy, may mediate against it." -- what foresight!
There's been some talk -- Nadler said back in April: "Someone is in contempt of Congress, you send the Sergeant at Arms and you arrest them. Alternatively you fine him $20,000 a day, whatever. We could do this." Since then, multiple witnesses have either refused to show up or refused to answer questions. There's rumors they're considering contempt for Lewandowski. No mention of fines or jail, though -- could just be the toothless kind of contempt they've used before against Barr (which relies on Trump's DoJ to prosecute, unlike congress' inherent contempt powers). But why let Trump dictate who has to comply with a house subpoena?
Why haven't house democrats revived their inherent contempt powers? It's certainly not because of senate republicans.