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White House officials said Tuesday that some Blue Dog Democrats have privately promised to vote for health reform despite their previous opposition.

Utah Rep. Jim Matheson isn't one of them, but the conservative Democrat hasn't ruled out supporting President Barack Obama's signature bill in a make-or-break vote slated for late this week or early next week.

Matheson opposed his party's health reform efforts twice before but says he is now undecided, hinging his vote on what changes are made in the final bill, which is modeled on the Senate version of reform.

Despite being an undecided vote, Matheson hasn't received any one-on-one attention from the president or Nancy-Ann DeParle, the director of the White House office of health reform, according to his staff. He did attend a White House reception with a number of other House members in honor of the passage of a new budget rule and health reform came up in conversation as people mingled.

Obama has vowed to do everything in his power to get the bill through Congress and that has included leaning on hesitant Democrats in a series of calls, one-on-one meetings and even private chats aboard Air Force One. The president summoned a few Democrats to the White House on Tuesday to talk about health reform.

In a briefing with newspaper reporters, DeParle expressed confidence that more Blue Dogs will back the bill this time around, saying some had already committed to do so, though she wouldn't name names.

"I'm optimistic that many of the Blue Dogs who voted no will be voting yes this time," she said.

Of the 54 Blue Dog caucus members, 25 of them opposed the House version of health reform in a vote last November. Some have promised to continue opposing the bill, such as Rep. Stephanie Herseth Sandlin, D-S.D., one of the three Blue Dog caucus leaders, while others say they haven't made up their minds. The Blue Dogs are moderate and conservative Democrats who are concerned primarily about fiscal issues.

Matheson, who is the Blue Dog spokesman, has said he is concerned about the bill's estimated $950 billion price tag, which is covered through a series of targeted tax increases and savings from within federal health programs. He wants to make sure the bill does enough to slow medical inflation as well.

DeParle, who considers herself a Blue Dog, said the final health reform compromise should be an easy sell to these conservative Democrats, since it meets the criteria they publicly announced last May. Those principles included not adding to the deficit, reducing waste in Medicare, strengthening the role of primary care doctors and giving small businesses a targeted tax credit to cover rising health costs.

"It has the provisions they are looking for," DeParle said. "They wanted long term cost containment, they wanted something like the tax on high cost plans to really do something on the demand side. I think the bill meets those principles."

But another reason some Blue Dogs are skittish is that the Obama plan is not popular in their districts, many of which lean Republican.

The White House is encouraging these Democrats to campaign on the "immediate deliverables" in the reform bill. Those include a new high-risk insurance pool for people who can't get coverage because of a pre-existing condition and limits on unpopular insurance company practices, such as caps on lifetime benefits or the ability to drop the coverage of someone who gets sick.