Senate Majority Whip Dick Durbin (D-Ill.) said Tuesday that Democratic leaders will make a renewed push for party unity on procedural votes, now that the majority is 60 votes strong.

Because 60 votes are needed to beat back a filibuster, Durbin said Democrats need to “stick together,— particularly on votes to bring up crucial Democratic agenda items like health care reform and climate change legislation.

“Believe me, this is not a binding rule in the Caucus,— the No. 2 Senate Democrat 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. There can be a lot of disagreements and a lot of different amendments offered. Members can take their positions, but let’s keep this moving forward.—

Sen. Al Franken’s (D-Minn.) formal induction into the Senate on Tuesday gave Democrats their 60th Caucus member.

Still, Durbin said Democrats would continue to reach out to Republicans, as they did when they didn’t have a filibuster-proof majority, in order to make up for Democrats who defect or who are absent. For example, two Democratic Senators — Edward Kennedy (Mass.) and Robert Byrd (W.Va.) — have missed a lot of votes in the past few months while they battle illnesses.

“People just think it’s magic that we just elected the 60th Democratic Senator. It’s not,— Durbin said. “I have to sit down … one by one and persuade [Democrats] to be joining us in the 60-vote requirement. … People now think, Oh, you have 60. You don’t have to talk to the other side of the aisle.’ I don’t subscribe to that. I’ve already started reaching out as everyone in our Caucus has, at least at the leadership level, to find Republicans who will help us with key issues like health care reform.—