Senate Judiciary Chairman Patrick Leahy (D-Vt.) supported McConnell's confirmation and complained prior to the vote that arguments from Republicans were slowing down the confirmation process.
“There was no need for cloture to be filed on this nomination,” said Leahy.
"Why was the Senate not able to reach a time agreement to debate and vote on this nomination last year?" he asked.
Senators objected to the nomination in part because of McConnell's career as a trial lawyer, during which he collected millions of dollars as part of civil cases against lead paint manufacturers and tobacco companies.
Some Republicans also objected to the fact that McConnell had donated about $700,000 to the Democratic Party over the years.
The Senate adjourned at 6:59 p.m. on Wednesday and is set to return at 10 a.m. on Thursday.