House Democrats appeared to inch closer to a plan for action on President Barack Obama’s $858 billion tax cut deal, even as they continued to vent Tuesday night about the proposal he negotiated with Senate Republicans.

The Senate is scheduled to hold a series of votes on the measure midday Wednesday, and Senate Minority Leader Mitch McConnell (R-Ky.) warned dissatisfied House Democrats against making changes to any Senate-passed version of the measure.

But Rules Chairwoman Louise Slaughter (D-N.Y.) said her committee might offer two or three changes, including one rolling back an estate tax provision, in the form of a rule. “I don’t think we’re basing what we want to do by a threat by Mr. McConnell,” she said. The House could vote on the tax cut bill as early as Wednesday afternoon.

Rep. Chris Van Hollen (Md.), who has been the House Democrats’ lead negotiator on the package, questioned whether Senate Republicans would really stand in the way of the package’s other provisions to protect a $25 billion estate tax cut for 6,600 families next year.

He said it’s not yet clear what Democrats will do. “We’ll digest the comments overnight and come back with a recommendation,” Van Hollen said.

Rank-and-file Members remain frustrated with the plan.

Rep. David Wu ripped the administration for not fighting harder. “There’s no need to negotiate with an administration that won’t fight,” the Oregon Democrat said. “This administration fought on nothing. It stands for nothing. And if they keep going down this road, they are going to get steamrollered by Darrell Issa and a Republican majority for the next two years.”

Wu added: “Ronald Reagan was effective for eight years when he put a bunch of air traffic controllers out on the street for good. Bill Clinton didn’t get his street cred until he jammed Newt Gingrich.”

Wu said he agreed, at the request of Caucus Chairman John Larson (D-Conn.), to pull a resolution stipulating that the House would only consider legislation that would extend unemployment benefits at least as long as it extends tax cuts for the wealthy. Wu’s resolution had been slated for consideration Tuesday night.

Rep. Peter DeFazio (D-Ore.), who led a successful drive last week to get the Caucus to vote against taking up the bill without changes, said he and others thought the leadership had squandered the opportunity to make a solid case for the House Democrats’ position.

“We enabled our leadership, we gave them an opening, and I feel — with the exception of Mr. Van Hollen pounding on the estate tax — they have failed to use that opening to push back against the McConnell-Obama deal,” DeFazio said, adding that other Democrats expressed the same complaint at Tuesday night’s Caucus meeting.

Democrats were also concerned about the effect of the legislation on the Social Security Trust Fund, he added.

“You don’t start draining money out of Social Security like it’s a piggy bank to give tax cuts,” DeFazio said.

“We’re still in a dilemma,” Rep. Sheila Jackson Lee (D-Texas) said. “My point is the House is not irrelevant.”

The proposal would schedule the tax cuts to expire at the end of 2012, and Jackson Lee said she would like to hear from the White House about how it will respond if Republicans press for another extension in a presidential election year. “I’d like to hear the president is going to veto this in 2012,” she said of the tax cuts for the wealthy.

Obama has called some Members to urge support for the plan, including Rep. Elijah Cummings (D-Md.), who said Tuesday night that he is still leaning against supporting the plan because of the tax cuts for the wealthy and other concerns.

Obama told Cummings that he would campaign on letting the tax cuts for the wealthy expire, but Cummings said he questioned whether that was the best timing politically.

Some Members want to amend the package to extend unemployment benefits for two years, not one, to provide parity with the tax cuts, Cummings said. Others want votes to modify the estate tax provisions.

“Right now it’s a question of how much can be changed without ruining the president’s effort to get this thing passed,” Cummings said. “We’re getting a message of urgency from a lot of people.”

Anna Palmer contributed to this report.