Washington Post blogger Greg Sargent, who is well-connected with Senate Democrats, reports that they now fear the death of 89-year-old New Jersey Democrat Frank Lautenberg earlier this month has undermined their plans to change the Senate’s filibuster rule.

The rule requires the assent of 60 lawmakers before debate can continue on a bill. This has frustrated Democrats to no end since it enables a minority of Republicans to stymie their agenda. Senate Majority Leader  Harry Reid, D-Nev., has often talked about getting rid of the rule, which would require a majority itself.

But not all Democrats are on board with that, especially several longer-serving ones who’ve seen the Senate majority swing back and forth and know what it is like to be in the minority themselves. According to Sargent’s sources, Lautenberg was the 51st vote Reid needed to make the change:

Here’s what this means: A very plausible scenario being mulled by top Dems is that the prospects for changing the rules may rest on a tie-breaking Senate vote from Vice President (and Senate president) Joe Biden.

It’s simple math. Lautenberg’s passing means Dems now only have 54 votes in the Senate. (His temporary Republican replacement can’t be expected to back rules reform.) Aides who are tracking the vote count tell me that Senator Carl Levin (a leading opponent of the “nuke option” when it was ruled out at the beginning of the year, leading to the watered down bipartisan filibuster reform compromise) is all but certain to oppose any rules change by simple majority. Senators Patrick Leahy and Mark Pryor remain question marks. And Senator Jack Reed is a Maybe.

If Dems lose those four votes, that would bring them down to 50. And, aides note, that would mean Biden’s tie-breaking vote would be required to get back up to the 51 required for a simple Senate majority. That’s an awfully thin margin for error.

It would also mean the Democrats would have to decide to change the rules in a radical way without an actual majority — a power play that may not look good for them no matter how much they slam Republicans for obstructionism.