Conrad, appearing on the "Charlie Rose Show" on PBS, said that senators should not count on Sens. Robert Byrd (D-W.Va.) or Edward Kennedy (D-Mass.) to force through controversial legislation.
"The Democrats have 60 votes in the United States Senate. That's true," Conrad said. "Senator Kennedy and Senator Byrd have been absent due to illness for an expended period of time."
Conrad said that while senators respect Kennedy and Byrd, and hope for their quick recovery, they cannot be expected to show up for the rounds of votes in the Senate which sometimes see dozens of votes at a time.
"So, I don't think you can count on both of them being there for that entire proceeding," Conrad said. "So that takes you to 58 votes."
Kennedy has been suffering for brain cancer for which he's being treated, while Byrd has suffered a variety of maladies, including a recent extended hospitalization for a staph infection.
Conrad said that as a result of Byrd and Kennedy's absence, senators should be more committed to bipartisan legislation on healthcare, warning that using budget reconciliation to pass a reform bill would result in "Swiss cheese for legislation."