Unlike the Senate budget resolution, the House resolution includes "reconciliation" instructions that would protect a bill from the filibuster that can thwart legislation in the Senate even if it has majority support. It is understood that the reconciliation procedure would be used to enact health care reform.
Opponents of the President's agenda have been surprisingly effective at casting as unfair the procedure that would allow legislation to be enacted by a majority vote in both chambers. The media has in many cases uncritically quoted lawmakers who feel it would be partisan and divisive to allow the Senate to approve a bill with only 59 out of 100 members voting in favor.
Some have complained that reconciliation is only to be used for deficit-reduction, but these are largely the same members who voted in favor of reconciliation bills during the Bush years that actually increased the deficit by cutting taxes. Even putting that aside, it's not clear that the original purpose of reconciliation is any more important than the original purpose of the Senate filibuster, which was originally used only on rare occasions but has turned into a 60-vote requirement to pass any bill introduced in the Senate.
It's true that there are rules limiting what sorts of measures can be enacted through the reconciliation process. (Provisions that have no quantifiable budget impact in the next few years may be impossible to pass through reconciliation.) But the limits imposed by a potential filibuster may be greater. Whether health care reform happens at all hinges on whether or not Congress can raise the revenue to pay for it. Hopefully, bipartisan agreement can be found on how to do that. But Congressional leaders would be smart to leave themselves the option of reconciliation in case such consensus proves elusive.