Coverdell, a congressional workhorse who quickly ascended to a leadership post and served as the Senate point man for longtime friend George W. Bush, died Tuesday, a day after surgery to relieve pressure from a cerebral hemorrhage. He was 61.
A vase of white flowers sits on Coverdell's desk in the Senate as colleagues mourned the late GOP leader.
Arizona Sen. Jon Kyl said, "If ever there was an indispensable senator, Paul was it."
Tennessee Sen. Bill Frist said the country has lost one of its
"most principled leaders."
In his invocation, Senate Chaplain Lloyd Ogilvie called Coverdell an "outstanding legislator."
Coverdell's death means Georgia likely will be represented by two Democrats in the U.S. Senate, at least until a special election can be held.
Under Georgia law, the state's Democratic governor, Roy Barnes, will appoint an interim replacement until a Nov. 7 special election.
Barnes has said it is "inappropriate" to discuss any appointment so soon after Coverdell's death. But Eric Johnson, the Georgia Senate Republican leader, said Barnes will almost certainly appoint a Democrat in an effort to handpick the next senator.
Democratic Party sources said a handful of names already are circulating. Among those mentioned are Great American Cookie Co. co-founder Michael Coles, who ran unsuccessfully against Coverdell in 1998; former U.S. Rep. Buddy Darden; Secretary of State Cathy Cox; Attorney General Thurbert Baker; U.S. Rep. Sanford Bishop; state Sen. Charles Walker; and state Rep. Larry Walker.
On Tuesday, President Clinton lauded Coverdell's work as an advocate for education and in the fight against illegal drugs.
"Paul Coverdell spent a lifetime serving the people of Georgia and our country," Mr. Clinton said in a statement. "I join all Americans in honoring Paul Coverdell for his years of service as a soldier, a public servant and a statesman."
Coverdell, who served as Peace Corps director in the Bush administration, was first elected to the Senate in 1992 after defeating incumbent Democrat Wyche Fowler Jr.
He became the fourth-leading Republican in the Senate, serving as GOP Conference secretary and sitting on several committees, including agriculture, finance and foreign relations.
He also was the Senate liaison for George W. Bush's presidential campaign and had been busy preparing for the Republican National Convention, which begins in Philadelphia in two weeks.
"Paul Coverdell was one of the kindest and most decent men I met in my entire life," former President George Bush said in a statement.
Added Bush's son, the Texas governor: "Paul's soft-spoken, hard-working ways will be sorely missed by all of us who knew him and loved him."
Coverdell built reputation as an effective, behind-the-scenes operative for Senate Republicans, working long hours to organize his colleagues into a unified voice. He became a close ally of Sen. Trent Lott, R-Miss., and worked his way into the Senate GOP leadership after Lott became majority leader in 1996.
Lott was emotional, choking back tears as he announced Coverdell's death to the Senate on Tuesday, reports CBS News Correspondent Ed Crane.
"At the appropriate time I will join the rest of my colleagues and try to make appropriate remarks to pay tribute to Paul, but for now I can't do any more than make this announcement," said Lott.
Coverdell was born Jan. 29, 1939 in Des Moines, Iowa, and received a bachelor's degree in journalism in 1961 from the University of Missouri.
He served two years in the Army in Okinawa, Korea and Taiwan before returning and helping his parents start the family's Atlanta insurance and financial services business, Coverdell & Co.
He was married to the former Nancy Nally of Sandy Springs. They had no children.
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