WASHINGTON – Nine House Democrats indicated in an Associated Press survey Monday they have not ruled out switching their “no” votes to “yes” on President Obama’s health care overhaul, brightening the party’s hopes in the face of unyielding Republican opposition.

The White House tried to smooth the way for them, showing its own openness to changes in the landmark legislation and making a point of saying the administration is not using parliamentary tricks or loopholes to find the needed support.

Democratic leaders have strongly signaled they will use a process known as “budget reconciliation” to try to push part of the package through the Senate without allowing Republicans to talk it to death with filibusters. The road could be even more difficult in the House, where Speaker Nancy Pelosi is struggling to secure enough Democratic votes for approval, thus the effort to attract former foes.

The White House said Obama will outline his final “way forward” in a Washington speech Wednesday, and he is expected to embrace a handful of Republican ideas for making health care more efficient.

Few in Washington think those gestures will be enough to persuade a single House or Senate Republican to embrace the legislation. But they could give wavering Democrats political cover by showing the party has been willing to compromise, ammunition against campaign accusations this fall that they rammed the bill through Congress with no regard for other views.

The proposal would impose new restrictions on insurance companies and order health insurance coverage for as many as 30 million Americans who now lack it.

Persuading lawmakers to change their votes is a tough sell. Elected officials are loath to vote two ways on a controversial issue, feeling such a switch draws more resentment than support overall. Democratic leaders stress that the legislative package soon to reach the House will be less expensive than the one that passed in November and will contain no government-run program to compete with private insurers.

They hope those changes will give additional cover to party moderates thinking of switching from no to yes.

In interviews with the AP, at least nine of the 39 Democrats either declined to state their positions or said they were undecided about the revised legislation, making them likely targets for intense wooing by Pelosi and Obama. Three of them — Brian Baird of Washington, Bart Gordon of Tennessee and John Tanner of Tennessee — are not seeking re-election this fall.

The others are Rick Boucher of Virginia, Suzanne Kosmas of Florida, Frank Kratovil of Maryland, Michael McMahon of New York, Scott Murphy of New York and Glenn Nye of Virginia. Several lawmakers’ offices did not reply to the AP queries.

Both parties have used the “reconciliation” strategy to pass big bills before, but Republicans call the health care push an unwarranted departure from standard practices.

Top Democrats are reminding colleagues and voters at home that the Senate already has passed its version of the health care bill on Christmas Eve with a super-majority of 60 votes, which squelched a GOP filibuster without resorting to reconciliation rules. The new plan calls for the House to pass that same bill and send it to Obama.