The top three Democrats in the Senate. (REUTERS/Jonathan Ernst)

So much for a neat, orderly succession.

Sen. Charles E. Schumer (D-N.Y.) and Richard J. Durbin (D-Ill.) were at odds Tuesday over the future of the Democratic whip position, just days after Minority Leader Harry M. Reid (D-Nev.) triggered a leadership shuffle with his retirement announcement. Durbin's office said Schumer vowed to support Durbin staying on as whip, the No. 2 position in leadership, in the next Congress. Schumer's office said he made no such assurance.

The surprisingly contentious feud between two longtime housemates has swiftly called into question whether Senate Democrats can resolve their hierarchy issues neatly or whether they are facing a messy intra-party fight heading toward 2016.

The dust appeared to settle quickly in the wake of Reid's retirement, which he announced Friday. Reid swiftly backed Schumer, currently the third-ranking Democrat, to succeed him as leader in an interview with The Washington Post. Later, Durbin also voiced support for Schumer to become leader in an interview with The Post.

But a conversation that took place hours earlier -- on the sidelines of the Senate's all-night budget "Vote-a-rama" -- has become the source of intense dispute.

According to Durbin's office, Durbin and Schumer came to an agreement during that chat in anticipation of Reid's announcement.

"The two senators agreed to support each other -- Schumer for leader, Durbin for whip," said Durbin spokesman Ben Marter. "They shook hands. That was the interaction."

But Schumer spokesman Matt House denied that his boss agreed to back Durbin for whip.

"That never happened, and they know it," House said.

Marter said Reid told Durbin Friday morning that he would support him for whip. Reid's office did not immediately respond to a request for confirmation of that exchange late Tuesday.

While there is no race for whip, as Durbin is the only one who has said he plans to run, a wild card is Sen. Patty Murray (Wash.), currently the fourth-ranking Senate Democrat. Murray has not ruled out the possibility of running for whip.

The offices of both Murray and Durbin said the two spoke Tuesday morning but did not say whether the whip position came up in the conversation.

"Senator Murray is focused on her current job and isn't going to be speculating about other positions under Senator Schumer in leadership elections two years from now," Murray spokesman Eli Zupnick said in an e-mail.

Leadership elections for the next Congress will be held shortly after the November 2016 election.