Senate Democratic leaders have stepped up the pressure on their rank and file to unify on procedural votes after finally gaining a filibuster-proof majority, but centrists who have long been headaches for the leadership are so far refusing to commit to the strategy.

“Most Senators vote their conscience and they do what they think is right. They didn’t come here to be told what to do by somebody else,— moderate Sen. Evan Bayh (Ind.) said.

Majority Whip Dick Durbin (Ill.) said Tuesday that he and Senate Leader Harry Reid (Nev.) will be asking the 60-member Democratic caucus to “stick together— on procedural votes that would allow the chamber to begin or end debate on legislation. Sixty votes are needed to close debate, or invoke cloture, on a measure and avoid a filibuster.

The message to Democrats, Durbin said, is: “Don’t let the Republicans filibuster us into failure. We want to succeed, and to succeed we need to stick together.—

Both parties have always put a premium on unity when it comes to procedural votes. The difference in the 111th Congress is that a unified Democratic Conference doesn’t necessarily need Republican support to succeed.

With 60 caucus members, Senate Democratic leaders are now under increased pressure to deliver big legislative wins on health care and climate change, largely because Republicans theoretically can no longer use the filibuster rules to prevent Democrats from passing major pieces of the agenda.

Plus, if Democrats fail to get cloture on health care reform, for example, the media blame game is unlikely to focus on wayward Republicans but rather on Democratic infighting and a lack of party unity.

Though Reid and other leading Democrats have downplayed the strength they have now that Sen. Al Franken (Minn.) has been sworn in as the 60th member of their caucus, Democrats said they want to capitalize on their numbers as much as possible and that procedural votes are their only hope for unity, given the disparate views of the Conference.

[IMGCAP(1)]“Not everybody will be united on legislation, but maybe we can get everybody united on process and procedure,— said one senior Senate Democratic aide, who added that the goal is to unite the caucus on the general agenda if not the specifics.

But many Senate Democratic centrists remain leery of voting for any Democratic agenda item that could put them in jeopardy in their conservative-leaning states.

For example, Sen. Mary Landrieu (La.) said she would “be supportive of many Democratic priorities— and is “absolutely committed to help the Democratic leadership and the president get health care reform that our people can depend on.— However, she flatly refused to rule out filibustering any bill, including health care and climate change legislation.

“I’m going to keep an open mind, but I am not committing to any procedural straitjackets one way or another,— she said.

Similarly, Sen. Ben Nelson (Neb.) said he has often been loath to block legislation or executive branch nominees, but reserves the right to filibuster if he determines it’s warranted.

“I’m not a closed mind on cloture, but if it’s an abuse of procedure, if it’s somebody trying to put a poison pill into a bill, or if it’s something that would be pre-emptive of Nebraska law, or something that rises to extraordinary circumstances, then I’ve always reserved the right to vote against cloture,— Nelson said.

He noted that it might make a difference to him if the vote is on bringing a bill up for debate rather than ending debate, but he said he would not rule out a filibuster in either case.

Bayh said asking Democrats to be unified on procedural votes was akin to asking them to violate their principles in some cases.

“You know how this place operates. Very often, it’s the procedural votes that determine the substantive outcome. Sometimes not, but it’s not uncommon that that is the case. So those votes on procedural issues will be cast as if they are the ultimate substantive vote,— he said.

But Durbin said that moderates, such as Bayh and Nelson, have voted with Democrats on procedural issues many times before.

“They may vote against final passage on a bill. They may vote with Republicans on amendments,— he said. “But on this idea of allowing the filibuster to stop the whole Senate, I think, we have persuaded them more often than not that they shouldn’t let the Republicans control our agenda. We ought to control our own agenda.—

Reid went further on Tuesday confidently predicting that, “On procedural votes, we’ll keep Democrats together.—

Reid and Durbin placed a special importance on the looming health care debate; the Majority Leader is hoping to bring a bill to the floor by July 20.

“Believe me, this is not a binding rule in the caucus,— Durbin said. “It’s just a plea to our Members that if we’re going to face an historic vote on health care reform, we’re urging Democratic caucus members to support us on the procedural issues.—

In the meantime, Durbin and Reid continue to say they will not stop courting GOP votes or looking for bipartisanship on major legislation. Of course, that could come from necessity, given that two Senate Democrats — Edward Kennedy (Mass.) and Robert Byrd (W.Va.) — have been absent from the chamber for months as they battle illnesses.

If both or either Senator continues to miss votes, even a fully unified Democratic caucus will be unable to prevail without GOP support.