He shall have power, by and with the advice and consent of the Senate, to make treaties, provided two thirds of the Senators present concur...
Even with the D's in control, that may be a tougher threshold to achieve.
Nah, you just have to think evil like a Democrat! A quorum of the Senate only needs 51 present. If you have a quorum, you can have a legal seating and call-to-order of the Senate to conduct business.
Here's the plan:
Organize a Democratic Senate meeting. Democrats only, and you only need the safest 51 seats; let the 9 "potentially lost" seats out. At this meeting, vote to open session, since you have a quorum. At this point, the Democrat-only meeting is a legal and fully-recognized meeting of the Senate.
Then you need 2/3rds of the Senators present to approve - that's just 34 votes needed!
See, it's really easy to do - no need to worry about the pesky GOP, and you only need 34 of the safe seats to actually vote! Yes, you can actually pass a "2/3rds majority" clause with just 1/3rd of the Senate voting affirmative.