WASHINGTON (AP) — Days away from a make-or-break vote on his health care overhaul, President Barack Obama is turning up the pressure as only presidents can, as Democratic leaders make a desperate scramble for votes.

The president is wooing freshman Democrats in the Oval Office, holding at least two one-on-one sessions in the past few days that never appeared on his official schedule, according to aides to two lawmakers invited, Reps. Scott Murphy, D-N.Y., and Suzanne Kosmas, D-Fla.

Both voted “no” when the legislation passed the House on the first go-round last year, but now they’re not ruling out siding with the president and Democratic leaders on what’s expected to be a cliffhanger vote in the House later this week.

Another lawmaker who opposed the legislation last year, Rep. Dennis Kucinich, D-Ohio, flew with Obama on Air Force One to an Obama appearance in Kucinich’s district Monday. Kucinich, was against the bill because he wants a larger government role in health care, also is not ruling out voting “yes” this time.

With a number of anti-abortion Democrats expected to defect over provisions they contend allow federal funding of abortion, every vote will count for Democratic leaders, who need to win over lawmakers who opposed the legislation the first time — and keep reluctant supporters on board in the face of escalating attacks. Sweetening the pot, those who vote with the president may get more help from him in the future: Party officials said that in determining how to allocate Obama’s time for campaign stops or other events, a vote on something like health care would be a consideration.

House Democrats triggered the countdown Monday for the climactic vote, with the House Budget Committee agreeing 21-16 to fast-track rules for the health bill, a necessary first step before floor action. Even so, the legislation remained incomplete. House Democrats caucused Monday evening, and a number of rank-and-file lawmakers straggled out discouraged that they still didn’t have final legislative language or a cost estimate from the Congressional Budget Office.

Leaders hope to get both those things Tuesday. Until then there’s only so much they can do to pin down wavering lawmakers who will soon be asked to make one of the riskiest votes of their careers.

“There’s no decision yet on what the process is going to be, there’s nothing back from the CBO, there’s no commitment yet from the Senate that they can get 51 votes, and there’s no bill to show me what it’s in it,” said Rep. Dina Titus, D-Nev., a freshman who voted “yes” last year and has been targeted by Republicans. “So until those things get resolved I’m staying uncommitted.”

Democratic leaders sounded notes of optimism anyway.

“When we bring the bill to the floor, then we will have the votes,” said Speaker Nancy Pelosi, D-Calif.

Obama said in an interview with ABC News: “I believe we’re going to get the votes. We’re going to make this happen.”

In order to avoid a Republican filibuster in the Senate, the House will be voting to approve the Senate’s health overhaul bill, along with a package of fixes to change things House Democrats didn’t like, such as a tax on high-value insurance plans. That fix-it package can pass the Senate with a simple majority, a necessary approach because Republicans are unanimously opposed and Democrats control only 59 Senate votes, one short of the 60 needed to block a filibuster.

A complicated procedure is being contemplated for the House floor, too, one that would shield lawmakers from having to vote directly on the Senate bill, allowing them to instead approve a rule for debate that would deem the Senate bill passed once the fix-it bill has passed.

Outside interests on both sides turned up the heat.

Union groups and other supporters announced a $1.3 million advertising campaign urging 17 House Democrats to vote for the measure, and officials at the Service Employees International Union threatened to withdraw support from Democrats who vote against the bill.

The National Right to Life Committee, which opposes abortions, wrote to lawmakers that support for the Senate bill would be a “career-defining pro-abortion vote.” Although House leaders hope to get the votes they need without changing the abortion language, House Energy and Commerce Chairman Henry Waxman, D-Calif., said Monday that he’d spoken during the day with Rep. Bart Stupak, D-Mich., leader of a group of anti-abortion Democrats, and would continue their conversations.

It was more than a year ago that Obama asked Congress to approve legislation extending health coverage to tens of millions who lack it, curbing industry practices such as denying coverage on the basis of pre-existing medical conditions and beginning to slow the growth of health care costs nationally.

Sweeping legislation seemed to be on the brink of passage in January, after both houses approved bills and lawmakers began working out a final compromise. But those efforts were sidetracked when Republicans won a special election in Massachusetts — and with it, the ability to block a vote on a final bill in the Senate.

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Associated Press writers David Espo, Ben Feller, Ricardo Alonso-Zaldivar, Alan Fram, Charles Babington, Ann Sanner and Sam Hananel contributed from Washington. Seanna Adcox contributed from South Carolina.