WHITE HOUSE STILL SELLING TAX DEAL TO CONGRESSIONAL DEMS…. To put it mildly, the response to the tax policy agreement struck by the White House and congressional Republicans hasn’t been well received by congressional Democrats. On Tuesday, Vice President Biden took his pitch to his former Senate colleagues, and received little more than icy stares.

Yesterday, however, there was apparently some thawing.

Senate leaders are planning to begin debate on a far-reaching tax package as soon as Thursday as rank-and-file Democrats warm to an agreement between the White House and Republicans to extend a host of expiring tax cuts and pump fresh cash into the economy.

Democrats were still angry Wednesday about what they viewed as President Obama’s capitulation to GOP demands to preserve tax cuts for the wealthiest Americans, particularly a deal to exempt estates worth as much as $10 million from a revived inheritance tax. But lawmakers said the magnitude of the concessions Obama won came into sharper focus Wednesday as the White House highlighted independent forecasts predicting that the package could create as many as 2.2 million jobs next year.

While Biden’s sales job didn’t affect the caucus’ anger, the White House sent budget director Jacob Lew and senior Treasury adviser Gene Sperling to talk with Democratic senators yesterday, fielding questions and providing economic analyses. Afterwards, Senate Majority Whip Dick Durbin (D-N.Y. Ill.) said his members become “more open” to supporting the package.

The administration still has a much bigger problem in the House. Biden talked to House Democrats yesterday, who were even less receptive to the agreement than Senate Dems were the day before. The Post‘s report noted that Biden led a two-hour meeting, followed by “dozens” of Democrats lining up to “interrogate” the vice president on the deal.

Is the antipathy enough to kill the agreement? I haven’t seen any firm head-counts, and some still seem to think passage is a foregone conclusion, but anyone assuming the votes in the House are already in place is making a mistake.

“There remain very serious reservations on the House side. I think that there’s still a very serious question whether this package can pass in the form it’s in now,” Rep. Chris Van Hollen (D-Md.) said after the meeting with Biden.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.