Upvoted because this is the truth.
As a consultant, don't be an administrative burden for the client, be someone that gives them a feeling they can really stop worrying about their problem or task, because a real pro now has it in hand and it will magically get solved, and they will get the correct reports so that everyone is happy etc.
Ideally you let them imagine you are much, much better than anyone they've ever worked with, by rolling with that idea and not doing anything to detract from it. It's what they want to believe from the start, so you actually have some advantage from that. E.g. you can communicate when other people would avoid doing so, which often helps a business problem anyway, and you are likely to be presumed quite authoritative, even if you're secretly reading up on the material as fast as you can between meetings.
And be straight with the client if at all possible about issues, including whether you're being asked to do the right tasks, and manage yourself as if you had a great manager and PM so they don't have to. If necessary, help with gaps in managing other people too, but gently, by making sure people know bits of information that help, and taking small initiatives as long as they help. Overall be like you are wise, insightful, helpful, and understand engineering and businesses better than anyone they could hire normally, even if it's not really true.
I have just been a problem to two of my current clients, because of a timing conflict (and being messed around in a serious way by another company). That anguishes me and I'm now in repair mode. ethbr0's advice is exactly what I will be trying to get back to, and in the spirit of "be straight with the client" I will literally tell them that I understand why they hire a consultant, that I failed and have cost them (because I really have), and what I'm doing to rectify the problem. It's likely to work out fine, because once they (all the relevant people) feel that I really understand what they need, they're likely to stop worrying and be glad that someone else is making the problem magically disappear again. It will take about 1 meeting per person and some good deliverables, and a week or so for the network of managers talking to managers to calm down, until they feel that way, but me showing understanding and an aura of "humility, integrity and leadership" usually means they go back to all the other busy things occupying their time, confident I'm "on it" again.