A health bill won't pass the Senate unless members are confident it won't support abortion, a top Senate Democrat said Monday.

Sen. Kent Conrad (D-N.D.), the chairman of the Senate Budget Committee, said that an agreement had not yet been reached to satisfy enough members of the Senate that the health legislation won't subsidize terminating pregnancies.

"What we know for certain: If there is taxpayer funding of abortion in this bill, it goes down,"  Conrad said during an appearance on MSNBC. "That was the reality in the House; that's the reality in the Senate."

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"There has to be a way of working this out so we are left with something people can support," he added.

The House included an amendment from Rep. Bart Stupak (D-Mich.) in its bill over the weekend, a move to placate abortion rights opponents, but also one which angered House liberals.

Sen. Ben Nelson (D-Neb.) has said it's "highly unlikely" he'd support a Senate bill without similar provisions, while Sen. Susan Collins (R-Maine) said she opposes the Stupak amendment.

A deal in the Senate was "yet to be worked out," Conrad said.

"We've got to remember, this is not an abortion bill," the centrist Democrat added. "On the other hand, this bill will not advance unless people are convinced that there is not taxpayer funding for abortion."