As a solution, Reid will most likely not allow amendments on the oil bill he is introducing this week. His office has not yet announced this decision, but rumors are circulating to that effect. Reid's procedural history shows a fondness for this tactic, which he used to squeeze the health care bill through the Senate. When a Senate majority leader does not accept amendments, he is said to be "filling the tree." This phrase refers to a diagram in the Senate rule book that maps out how many amendments members can attach to a bill. The majority leader proposes amendments first, so if he fills all the branches of this tree with inane, place-holding proposals, other senators can't introduce amendments of their own. This tactic, however, does not preclude a filibuster and therefore must be used in tandem with cloture.
A Congressional Research Service report (PDF) from January found that Reid has resorted to this procedure more than any other Senate majority leader going back to 1985, though Republican majorities have relied heavily on it as well. Reid's habit of "filling the tree" demonstrates the paralyzing partisanship that characterizes this Congress. Reid fills the tree in order to prevent petty minority obstructionsim, but in doing so he does not allow for bipartisan formation of bills.
If Reid does decide to go this route with the oil bill, here's what the process would look like: he introduces the bill this week with a series of inconsequential amendments that prevent other senators -- including Rockefeller -- from proposing amendments of their own. He would then invoke a cloture vote and hope to round up 60 "yea"'s to push the bill through. After recess, he could consider granting floor time to Rockefeller's measure as a bill rather than an amendment, all the while knowing that Obama would veto it if it reached his desk.
The risk of "filling the tree," though, is that Reid's strong-armed tactics could piss off the senators whose votes he needs for cloture. The CRS report (PDF) found that between 2005 and 2008, the majority of amendment tree-filling attempts did not work. Over 50 percent of the time, the majority leader ended up pulling the bill from the floor or opening it to other amendments.
The oil bill, now that it's been stripped of its more contentious energy measures, is a fairly bipartisan measure. But alienating Democrats on an energy vote is never a good idea. If Rockefeller and his supporters interpret Reid's amendment-blocking as a reneging on his previous promise, they could decline to grant cloture, essentially dooming what should be a slam-dunk bill.