Murray and Ross Hutchins lost 7-5, 3-6, 6-3, 6-2 to Poland's Mariusz Fyrstenberg and Marcin Matkowski.
And if Murray and Dan Evans, a 19-year-old ranked 302 in the world, don't win both singles matches today, Britain will go down to the Cup's Europe/ Africa Group II, where they could come up against the likes of Monaco or Ireland.
Murray aggravated a wrist injury during his victory against Michael Przysiezny on Friday, and is doubtful for today.
The Scot said: "You can't tell until a few hours afterwards whether or not you have done an injury any harm, but I'm hopeful that it's okay.
"I can't say how close I came to not playing today. We talked about it and I thought I would just give it a try."
Murray and Hutchins squandered all but one of 19 break points they earned during the match, including six in the final game, in Liverpool.
Murray added: "That was terrible. You can't win matches by not taking chances on so many break points. They sometimes made it difficult on those points, but that is a terrible stat."
Coach John Lloyd said: "Dan is ready to go out there and win it. That's what Davis Cup is all about. I think he'll do it."
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