"There is simply no substitute for having a confirmed U.S. ambassador on the ground, reaching outside the wire to the Libyan people as they shape a safer, more productive and inclusive future," Menendez said.
At her confirmation hearing earlier this month, Jones promised to work to ensure sufficient security at U.S. facilities, saying the ambassador was the principle security officer and vowing to simply pick up the phone and call Washington if she felt security was lax.
If confirmed by the full Senate, Jones would take over an ambassadorship that has been vacant for nearly eight months.
The Obama administration's response to the attacks has been the subject of a long-running and bitter dispute with congressional Republicans. The GOP has accused the administration of trying to cover up details of the assault and its aftermath.
Senate Majority Leader Harry Reid, D-Nev., ratcheted up the political criticism on Tuesday, saying the GOP was hyperventilating about the Benghazi attack.
"It's about smear politics and nothing else," Reid told reporters.
He highlighted the Republican budget cuts, including the $300 million from the Obama administration's request of $2.6 billion for diplomatic and embassy security last year.
"Again and again Republicans have blocked, opposed or reduced embassy security funding .... so again, where is the outrage on this. The real fact is Republicans are more concerned about giving President Obama a black eye and taking shots at Secretary (Hillary Rodham) Clinton than actually tracking down the people who performed these outrageous acts of terrorism."
Privately, Democrats have expressed frustration with the administration's recent handling of the issue as new details from emails on Friday showed that political considerations influenced the editing of talking points used by U.N. Ambassador Susan Rice five days after that attack.