Trailing 1-0 after James Ward's valiant four-set defeat by Italy's star turn, Fabio Fognini, Murray was leading Andreas Seppi 6-4, 5-5 when play was called off last night because of bad light, rain having caused a lengthy delay earlier in the day.
Murray, who had to save four set points in the fading light, will resume his match with Seppi at 09.30 BST, facing a quick turnaround if he is to play doubles, with his reverse singles against Fognini to come tomorrow.
Captain Leon Smith admitted it will come down to how Murray feels as to whether he plays doubles, most likely with fellow Scot Colin Fleming. If not, Fleming and regular doubles partner Ross Hutchins will team up.
"It was a long, tough, challenging day," Smith admitted. "We'd rather be sitting here 1-1, Andy done and dusted and able to rest in the morning. It's not going to be easy but Andy's in the driving seat now. It should be livelier conditions so not physically too demanding. Then it's about having a discussion with Andy and the rest of the team to see what we do about the doubles."
Having struggled in the build-up to the tie with a stomach illness that caused him to skip practice on Wednesday, Murray looked strong against Seppi, recovering from 4-2 down in the second set before saving the four set points on serve at 4-5.
The key question for Murray is whether he is able, and willing, to play all three rubbers.
On a damp day at Tennis Club Napoli, right on the Bay of Naples with Mount Vesuvius looming in the background, and on a court that cut up badly at the back on one side, Murray had to wait several hours before getting on. Ward, whose heroics in the first-round win over the United States in San Diego had been pivotal in Britain reaching the last eight for the first time since 1986, performed admirably again as he pushed Fognini to four sets before going down 6-4, 2-6, 6-4, 6-1.
"I am very proud of James, " Smith said. "His level again was way ahead of his ranking and if he plays a deciding rubber, he should take a lot of confidence into that."