Sen. Mary Landrieu and President Barack Obama can link arms on many pieces of the White House's proposed budget package, including raising taxes on higher-income Americans and spending more on infrastructure.

But Ms. Landrieu, along with a notable handful of Democratic colleagues, parts ways with the White House on one increasingly thorny issue: the president's call to raise the estate tax as part of Washington's bid to strike a deficit-cutting deal before year's end.

"This particular tax is inherently unfair," Ms. Landrieu said, adding that she would oppose any year-end deficit-reduction package that raises the estate tax. "That's a make-or-break for me."

The Louisiana senator was joined by Democratic Sens. Max Baucus of Montana, who heads the Senate Finance Committee, and Mark Pryor of Arkansas, who said this week they would prefer not to raise the estate tax. They wouldn't say how an increase would affect their support for a broader agreement as the parties scramble to head off a package of hefty spending cuts and new taxes known as the fiscal cliff.

For more, see: Plan to Raise Estate Tax Divides Democrats