WASHINGTON — Just a few unsolved problems — and one final sales job — stand between House Democratic leaders and a landmark vote on President Barack Obama's promised remake of the nation's health care system.

Unfortunately for the Democrats, the unresolved issues are among the most vexing out there: abortion and immigration.

And although they're confident they'll succeed, Democratic leaders have yet to nail down the votes they'll need to pass their sweeping bill. They're aiming for floor action to begin as early as Friday and finish before Veterans Day, Nov. 11.

Or, as Majority Leader Steny Hoyer put it when asked when the House would take up the health care bill, "Friday or Saturday or Monday or Tuesday."

"We want to make sure it's correct," Hoyer, D-Md., told reporters Monday.

The 10-year, $1.2 trillion bill would extend coverage to tens of millions of uninsured Americans with a new requirement that almost everyone get insured, and give subsidies to help lower-income people afford plans. Businesses would be required to cover their employees, and insurance companies would no longer be able to turn people away because of their health status.

Democratic leaders unveiled the bill with fanfare last week, a 1,990-page plan that sought to satisfy the concerns of both liberals and moderates while combining separate health bills passed by three different committees over the summer.

House leaders have made progress winning over liberals to back a new government insurance plan in the bill that's weaker than what liberals preferred. But they haven't quite closed the deal with enough members of their caucus. An initial vote tally showed them falling short of the 218-vote majority they need, according to Democratic aides.

"The bill's improved," said Rep. Jason Altmire, D-Pa., one of many undecided lawmakers, citing fewer taxes and more deficit-reducing measures. But, Altmire said, "I'm not sure it's there yet."

Across the Capitol, senators are waiting to see the final language and price tag on a health bill that Majority Leader Harry Reid and a few other top officials wrote in secret. It's not clear when those details will be available and Reid, D-Nev., may not be able to begin debate on the issue until the week before Thanksgiving.

Determined to avoid being accused of not reading their bill, House Democrats met late Monday to do just that, going over the legislation section by section in a room in the basement of the Capitol.