“Ms. Haspel’s role in overseeing the use of torture by Americans is disturbing,” Mr. McCain wrote in a statement Wednesday night. “Her refusal to acknowledge torture’s immorality is disqualifying.”

With Mr. McCain absent from the Senate and unable to vote, and Senator Rand Paul, Republican of Kentucky, opposing Ms. Haspel, Senate Republican leaders will most likely need at least one Democratic vote for Ms. Haspel’s confirmation, and Senator Joe Manchin III, Democrat of West Virginia, has said he will support her. But if Mr. McCain can persuade at least one additional Republican to oppose Ms. Haspel, the nominee could be doomed.

That, however, is a big if.

Senator Jeff Flake, Mr. McCain’s fellow Arizona Republican, said Thursday that he remained undecided about Ms. Haspel, though he said Mr. McCain’s views would have “considerable” weight.

“He’s the only one who’s been through this,” Mr. Flake said, adding, “I obviously share his views on torture, and I always have, so his views mean a lot.”

In a chamber where so much is determined along party lines, Mr. McCain appeared to find more support among Democrats than within his own party.

“People around here would be lying to you if they said that it didn’t weigh on them,” said Senator Claire McCaskill, a Missouri Democrat facing a tough re-election fight this fall. “I can’t imagine anybody who has more authority on this subject than John McCain — in the whole country.”

Ms. Haspel, 61, oversaw a secret prison in Thailand in 2002 while a Qaeda suspect was waterboarded there, and is also under scrutiny for her conveyance of an order from her superior to destroy 92 videotapes documenting harsh interrogations.