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Notes on power sharing: Daschle and Lott negotiated a deal that was difficult to sell to many of his Republican colleagues, who, quite naturally, thought that the VP's vote should give them majority control, as usual.
Lott recognized the chaos that would ensue in the absence of an agreement. Among other things, VP Cheney would have to hang around the Senate most of the time. (How history could have been different.)
Daschle and Lott managed to gain agreement on committee chairmanships (all to the Repubs), equal party representation on committees, allowing bills to come to the floor if blocked by tie votes in committee, and no filling of the amendment tree...
Notably, they agree to prohibit the filing of a cloture petition during the first 12 hrs of debate on any amendable measure. Along with a ban of filling the amendment tree, this protected the opportunity of senators to offer amendments.
I can imagine Schumer offering similar provisions to protect Repub opportunities to offer amendments in exchange for provisions that limit filibusters or makes them easier to circumvent. He was thinking about this kind of thing a decade ago.
