WASHINGTON — Speaker Nancy Pelosi mobilized House Democrats on Friday for a final effort to pass an overhaul of health care, predicting approval in the next 10 days with help from President Obama, who delayed a trip abroad to try to win over wavering Democrats.

The White House said Mr. Obama would begin his trip to Indonesia and Australia a week from Sunday, three days later than scheduled, allowing him to be on hand for what is shaping up as the pivotal period for his top domestic initiative. Mr. Obama will travel to Ohio on Monday to push for passage.

But even as the yearlong battle hurtled toward a conclusion, approval of the bill was hardly certain, so lawmakers were preparing for a week of arm-twisting and high drama. Although they have been debating the issue for a year, some House Democrats said Friday that they could not say how they would vote because they had not seen the final text of the legislation or an official estimate of its cost.

Some issues that could swing blocs of votes, like insurance coverage for abortions, remain unresolved. House Democratic leaders said they had suspended their efforts to reach a compromise with party members who oppose abortion and the use of federal money to subsidize insurance that includes coverage of the procedure. That could cost them the votes of some House Democrats who supported the health care bill in the fall after it was amended to impose tight restrictions on abortion coverage.