The symbolic action comes as Sinema has come under criticism from progressive groups in Arizona after she voted to uphold the filibuster in the Senate.
The president left a meeting with Senate Democrats pessimistic about a way forward on voting rights, as Sens. Kyrsten Sinema and Joe Manchin reiterated their opposition to changing Senate rules.
The Senate minority leader pointed to statements by two moderate Democrats who oppose ending the legislative maneuver. Both sides claimed victory, but the truce could be short-lived.
Getting rid of the legislative filibuster — the rule requiring at least 60 votes to advance a bill — is what many activists say is key to passing a progressive agenda. But not all Democrats agree.