Nadal got off to a sluggish start in his first-round match and needed a tie-breaker to capture the opening set against 85th-ranked Serbian Dusan Lajovic on Tuesday.
The Spaniard, who is renowned for his strict on-court routines, complained about the noise of the rowdy audience at his match, the din amplified by the closed roof on Arthur Ashe Stadium to protect the players from rain.
The 31-year-old Spaniard ultimately settled down to dispatch Lajovic 7-6(6) 6-2 6-2 but may need a better effort to advance past the 24-year-old Daniel.
Nadal should be fresher than his Japanese opponent, who will be working on short rest after defeating American Tommy Paul in five sets on Wednesday with Daniel edging the seesaw first-round battle 6-1 4-6 4-6 6-2 6-2.
With no rain forecast, the $100 million roof that contributed to Nadal's annoyance in the first round should be wide open.
Should Nadal complete an expected victory on Thursday, he will move one step closer to a possible showdown against long-standing rival, number three seed Roger Federer.
The tournament's two best-known players could meet for their first ever U.S. Open clash if they make it as far as the semi-finals, adding to a series that Nadal leads 23-14 in head-to-head encounters since their first in 2004.
(Reporting by Rory Carroll; Editing by John O'Brien)
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