Erica Werner, AP

A small number of House Democrats who opposed health overhaul legislation on the first go-round may be President Obama's most important constituency when he unveils a revised proposal. At least nine of the 39 Democrats who voted nay when the House passed sweeping overhaul legislation 220-215 in November, are now undecided or withholding judgment until they see the final product.

It may seem improbable that any lawmaker would want to switch his or her vote on the measure, courting the flip-flopper label after a year of controversy over legislation that's slid ever downward in polls. But it will almost certainly have to happen in order for House Speaker Nancy Pelosi to round up the votes necessary to pass the Senate's version of the legislation, along with a package of changes that the President will update.

The changes — designed to make the Senate bill more palatable to House Democrats by rolling back a tax on high-value insurance plans, among other things — would get through the Senate under controversial rules allowing for a simple majority vote. That's the only option for Democrats because they no longer control a filibuster-proof 60 votes in the Senate, and Republicans are unanimously opposed.

Obama's announcement on Wednesday is expected to be a freshened blueprint of the changes he wants made to the Senate's health care bill, updated with ideas that at least have the fingerprints of Republicans, possibly in the areas of medical malpractice reform and rooting out waste and fraud from the medical system.

That's not likely to win him any votes from Republicans, who want President Obama to tear up the existing bills and start over, but it could give wavering Democrats political cover by showing the party has been willing to compromise in the wake of last week's televised bipartisan health care summit.

With four vacancies in the House, Pelosi will need 216 votes. She would command exactly that many if all the remaining Democrats who voted yes in November did so again. But many lawmakers expect defections, especially of members who oppose federal funding for abortion and feel the Senate language is too permissive in that regard. For every yes vote that switches to no, Pelosi and the White House must persuade one of the 39 Democrats who voted nay in November to switch to yes.

Some of the top targets may be the nine lawmakers who told The Associated Press directly or through spokesmen that they're undecided or undeclared. Three are retiring and don't have to worry about getting punished by voters, and five others are freshmen, mostly in competitive districts — lawmakers whom Pelosi will give a pass on tough votes when she can, but might call on when a major piece of legislation hangs in the balance.

House Majority Leader Steny Hoyer said Tuesday he believes members of Congress who help pass legislation overhauling the system will be anxious to defend it to voters in the fall elections. The Maryland Democrat said on CBS's The Early Show that he thinks the public supports many key elements of a new medical care system, including affordable health insurance for all Americans and families.

Hoyer said there still is a chance that a retooled bill the White House will outline later this week can win passage and said the legislation already circulating has strong provisions aimed at containing spiraling health care costs. At its core is legislation that would extend coverage to 30 million uninsured Americans over 10 years with a first-time mandate for nearly everyone to buy insurance, and a host of new requirements on insurers and employers.

However, the package soon to reach the House will be less expensive than the one that passed in November and will contain no government-run insurance program to compete with private insurers, making it more appealing to some moderates. Since Thursday's summit, President Obama has been involved in a series of meetings in which the new White House proposal is being shaped.

One possible reason for the recent show of determination by Democratic leaders is that they have received polling data showing that while the general idea of health care overhaul fares poorly with the public, the specific elements of the effort score high marks with crucial independent voters.