It’s being privately discussed at the highest levels of the Democratic Party: The passing of Senator Frank Lautenberg has cast doubt on the ability of Senate Democrats to exercise the so-called “nuclear option” and change the Senate rules via a simple majority.

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.

As I reported here the other day, President Obama has privately reassured Harry Reid that he will support the Majority Leader if he decides to change the rules, which means Biden can be expected to break the tie in Democrats’ favor. Indeed, it’s hard to imagine that there wouldn’t be unity between Reid and the White House on this.

But the mere fact that Biden’s potential role as tie-breaker is being discussed underscores just how precarious the push for a change in the rules really is. And this makes things very tricky for Dems right now. They need to escalate the threat level in order to force Senate Republicans to drop their unprecedented opposition to Obama’s nominations. Currently they are expected to filibuster Obama’s pick as Labor Secretary and his choices to head the Consumer Financial Protection Bureau and the Environmental Protection Agency, and they are threatening to oppose his three nominations for the D.C. Circuit Court of Appeals. All of these are key to Obama’s ability to move his agenda forward. But the numbers are such that we simply can’t be sure whether Dems can make good on the threat to change the rules by hitting the nuke button. This could embolden Republican obstructionism further.

On the other hand, Democrats really may be able to muster that 51 votes, particularly since Biden is presumably available as a tie-breaker. And if Republicans do conclude Reid can’t get the votes and call his bluff by continuing with their current levels of obstructionism, Dems will have no choice but to try to change the rules — an effort that could sill succeed.

All of which is to say that while Lautenberg’s passing has put the Dems’ ability to change the rules in peril, it has also increased the potential for more brinksmanship — and more miscalculation. Anyone who is telling you they know how this is going to end is lying to you.

Greg Sargent writes The Plum Line blog, a reported opinion blog with a liberal slant -- what you might call “opinionated reporting” from the left.