At the same time, members of Dodd's staff are becoming increasingly involved in shepherding the legislation.
Later this month, Dodd may lead a markup of the bill, a technical process in which lawmakers on the committee debate amendments. Under normal circumstance, a markup is led by the bill's author.
Speaking to reporters Wednesday, Dodd said he was not replacing Kennedy. "Sen. Kennedy is the chairman," he said, describing his own role as "coordinator of activities." Dodd also emphasized that Kennedy was continuing to speak by telephone with key lawmakers and interest groups in the healthcare debate.
But, Dodd said Thursday, Kennedy's illness has slowed development of the legislation. It now appears the Senate Finance Committee may begin considering its version of a healthcare overhaul bill before Kennedy's panel completes its work.
The Massachusetts senator's continued absence also has fed growing anxiety on Capitol Hill about his ability to lead an intense legislative campaign this summer and fall.
"I don't know of any other lawmaker who has the standing with liberal groups that he has and can work with Republicans like me," said Sen. Orrin G. Hatch (R-Utah), a longtime friend.
"If he were here, he and I would be working something out. . . . I pray for him. I hope he comes back. But he has a terrible, terrible illness."
Kennedy, whose staff has provided few details about his disease or treatment, was diagnosed last year with malignant glioma, a particularly virulent tumor.
Though one of the most liberal members of the Senate, Kennedy has developed close personal relationships with many Republican lawmakers, including Enzi and Hatch. "Sen. Kennedy has done a remarkable job of encouraging cooperation to work across the aisle," Enzi said Thursday.
At the same time, the Massachusetts lawmaker retains unrivaled credibility with liberals who are clamoring for a more government-driven solution to the nation's healthcare crisis -- an approach that is anathema to Senate Republicans.
Some on Capitol Hill believe that Kennedy's involvement could be decisive in putting together a final healthcare package.
"I'm here," Dodd said before meeting with Obama this week, "replacing someone who is irreplaceable."
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noam.levey@latimes.com
Janet Hook in the Washington bureau contributed to this report.