Senate Majority Leader Harry Reid (D-Nev.) pledged Thursday "a simple up-or-down vote" on the health bill unveiled by the House today.

Reid praised the healthcare package released by House Democrats, which builds off the legislation the Senate had passed last December and makes a series of changes to it.

"The bill that the House introduced today moves us another important step closer to that reality," Reid said in a statement. "A simple up-or-down vote on its adjustments to the bill the Senate already passed would make our good bill even better."

The statement is meant to send assurances to wavering House Democrats that the Senate would look to vote on whatever passes the House as-is, quelling concerns that the Senate would renege on a vote, or make further changes.

Republicans have sought to foster doubts among House Democrats that the Senate would be successful in acting, vowing their own amendments and points or order to the House reconciliation bill once it's reached the Senate.

"Democrats understand the uncertainty that middle class families face, and we are fighting to put Americans back in control of their own health care," Reid said. "The President and Congressional Democrats have taken the time to get this legislation right, and we know that the time is now to complete our work."

House Energy and Commerce Committee Chairman Henry Waxman (D-Calif.) suggested earlier on Thursday that House leaders would work with Reid and top Senate Democrats to make sure the House health bill would have enough votes to make its way through the Senate, hopefully without amendment.