A primer on Contempt of Congress enforcement
https://www.democraticunderground.com/100212116082
There are three methods Congress can use to enforce a Contempt of Congress citation in response to a witness' refusal to respond to a subpoena. All of them share specific requirements to get the ball rolling and then branch out into three different processes.
First, once the subpoena is issued, the witness or holder of documents has to definitively refuse to comply. That means more than just saying they won't, but to take some affirmative step to defy the subpoena, such as fail to appear or produce the documents by the deadline.
In McGahn's case, although he signaled yesterday he wouldn't show up, he didn't trigger anything until he actually didn't show up at the appointed time today. He has now defied the subpoena.
The Judiciary Committee now must make some effort to get him to comply. It might be by letter (the much-derided "strongly worded" letter is mocked around here, but it performs a legal necessity), conversations with him or his attorneys to try to negotiate compliance, or some other method. This is necessary because, down the road, before upholding a contempt citation, a court will require a showing that Congress made a good faith effort to secure compliance prior to issuing the citation.
If those efforts fail, the House Judiciary would hold an executive meeting - aka "markup" - to vote on a contempt recommendation. Markups usually require several days notice and usually, the minority can request a one-week extension.
At the markup, the Judiciary Committee members will discuss the measure and then vote. If a majority of Members agree, the contempt recommendation will be referred to the floor to be voted on by the full House.
When that happens, the measure will likely be referred to the Rules Committee which will set out the parameters for debate (how long each side has, etc.) and the vote. That usually doesn't take long and there may be ways to avoid having to do a rule on a contempt vote ( I haven't looked into that). The debate and vote are scheduled and then the full House votes. Simple majority carries.
If the measure passes, the Congress has now officially cited the witness for contempt. At that point, there are three different avenues that can be taken for enforcement. The first is already a nonstarter, so there's no point in even trying, unless they just want to make a point. That would be to refer the citation to the US Attorney for DC and ask them to enforce the citation with an arrest or prosecution. Since the US Attorney reports to the Attorney General, that ain't gonna happen. So let's move on.
The next possibility is for Congress to exercise its "inherent contempt" power, a rare tactic, which Congress hasn't done in nearly a century, but is being seriously considered. That could mean imposing a fine or instructing the Sergeant-at-Arms to arrest the subject and bring them before the body to answer the contempt charge. If they still don't comply, they would be held in custody until they do or until a judge orders them released. While it's possible to do this, it would be very difficult to pull this off logistically in many instances. It might be easier for a McGahn, who is a private citizen. But it's not clear how the Sergeant-at-Arms would go about arresting the Attorney General or other federal official under 24-7 protection of federal agents and whose homes and workplace are virtual fortresses. It will be interesting to see what happens if they go that route.
The third possibility is to go to court and ask it to enforce the citation. If the court rules that the subject must comply, failure to comply would result in a contempt of court citation, in addition to the contempt of Congress. In such cases, the court could enforce by, among other things ordering the US Marshals to arrest a subject.
The bottom line is that contempt of Congress citations aren't simple things and Nadler can't just snap his fingers and throw someone in jail because they didn't show up this morning..
I hope this is helpful. You can read more about the enforcement of Contempt of Congress citations here:
https://fas.org/sgp/crs/misc/R45653.pdf and here:
https://www.reuters.com/article/us-usa-trump-congress-subpoena-explainer/explainer-how-hard-hitting-are-u-s-congress-subpoenas-contempt-citations-idUSKCN1SC1YE 
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