UPDATE: A senior House Source confirms to Fox News that "deem and pass is dead"

Developing..

Fox News has learned that House Democrats are considering dropping a controversial parliamentary ploy to pass the Senate's version of the health care bill before the House begins on a second "fix-it" resolution, known as reconciliation.

Senior House Democratic sources indicate that there is an ongoing discussion about dropping what's billed a "deem and pass" strategy. Democrats have signaled for days that they would probably use a procedural two-step to get the House to approve the Senate’s health care measure.

Many liberal Democrats don’t like the Senate bill. So the House Democratic leadership is considering a gambit that would approve the Senate bill while simultaneously giving the green light to bringing the reconciliation package to the floor.

In other words, the House could pass the Senate bill without having a straightforward, up or down vote on that issue.

Republicans crowed about this method, arguing that Democrats were trying to pass the bill in an underhanded manner.

“It’s unprecedented. It’s breathtaking,” protested Rep. Paul Ryan (R-WI).

But House Democrats say privately they could score a public relations coup by killing this strategy and doing things the old-fashioned way.

One senior aide characterized the chances of the Democrats handling the Senate bill the traditional way as “good.” Another said that the “probability (was) increasing.”

The House Democratic whip team, which counts the votes, mulled the idea at a closed-door meeting Saturday afternoon.

At a meeting of the House Rules Committee, one of the chief sponsors of the health care measure, Rep. Henry Waxman (D-CA) said he was “against the idea of deeming” and passing the bill.

The House must approve the Senate’s version of the heath care bill and President Obama must sign that legislation into law before the “fix-it” bill, known as reconciliation, can come into play.

House Democrats are still aiming for a series of final votes on health care Sunday.

Eve Zibel contributed to this report.