Washington (CNN) -- President Barack Obama's top aides on Wednesday defended the tax plan hammered out with Republican leaders, saying Democrats are coming around to the reality that the agreement contains plenty of good things despite proposals they dislike.

At the same time, senior White House economic adviser Larry Summers warned Congress that failing to approve the agreement could lead to a double-dip recession in 2011.

"If they don't pass this bill in the next couple weeks, it will materially increase the risk that the economy would stall out and we would have a double dip," Summers told reporters at a White House briefing.

Summers stressed that he was not predicting an actual double-dip recession, which is defined as a recession followed by a short-lived recovery and then another recession, but added the possibility would increase greatly without approval of the tax plan by the end of the year.

Senior White House adviser David Axelrod also noted "real consequences" for the American people if Congress failed to approve the package, which includes a two-year extension of Bush-era tax cuts set to expire at the end of the year, as well as 13 months of unemployment benefits and a cut of 2 percentage points in the payroll tax.

Democrats in both the House and Senate have criticized the agreement negotiated with congressional Republicans as too expensive and giving away too much to their political opponents.

Leaving a caucus meeting of House Democrats with Vice President Joe Biden on Wednesday night, Rep. Peter DeFazio of Oregon said Biden "made it clear that this was it" and no changes to the proposal would be accepted.

Well over half of the roughly two dozen Democrats who got up to speak at the meeting were strongly opposed to the deal, DeFazio said, including himself. The agreement shows that "Republicans won a game of chicken," he said, arguing that the White House compromised too quickly.

Rep. Frank Kratovil of Maryland, who lost his re-election bid last month, said he would vote for the agreement because the plan will help the economy. Kratovil warned that Democrats need to learn the lesson of the mid-term election -- that voters believe they "'took their eye off the ball" on the economy and must do what they can to prove they are listening now.

On the Senate side, Democrats showed more openness to the agreement, though party leaders in the chamber said they would seek changes to improve the deal.

"We're working those out with the administration," said Sen. Dick Durbin of Illinois, the Senate's second-ranking Democrat. Asked if the changes could undermine Republican support, Durbin said, "Well, of course, but we have to try to have a process (in which) senators can express themselves."

On Wednesday, Obama downplayed tensions among Democrats and told reporters he expects the deal will pass in the end.

"I think it is inaccurate to characterize Democrats at large as feeling, quote unquote, 'betrayed,' " Obama said. "I think Democrats are looking at this bill and you've already had a whole bunch of 'em who've said, this makes sense and I think the more they look at it the more of them are going to say this makes sense."

Obama, and later Summers, noted that economists were predicting the package of tax breaks and benefits would boost the economy in the next two years, particularly in a period of sluggish recovery from recession with unemployment at almost 10 percent.

Summers warned that failure to pass the bill now could reverse such positive predictions from analysts including Mark Zandi of Moody's Analytics. Echoing the views of other analysts at Goldman Sachs and elsewhere, Zandi now says that real Gross Domestic Product growth in 2011 "will accelerate to 4 percent, job gains will pick up to 2.8 million, and the unemployment rate will decline to around 8.5 percent by year's end."

According to Summers, a "set of downward revisions would commence" on Wall Street if the tax package doesn't pass by the end of the year, when tax rates are otherwise scheduled to increase to 1990s rates.

White House Press Secretary Robert Gibbs told reporters that Obama might go to Capitol Hill in coming weeks to lobby for the package in the final days of the lame-duck session of Congress. Biden has been the administration point person so far in Congress, meeting Tuesday with Senate Democrats and Wednesday with House Democrats.

Republicans generally appear supportive of the package, which the White House advisers noted gave them their two main priorities - an extension of the lower tax rates from the Bush era to everyone, including the wealthiest Americans, and setting a 35 percent estate tax only on inheritances of more than $5 million.

House Democrats vented their frustrations over Obama's tax proposal at a closed-door meeting Tuesday night, with rank-and-file members slamming the White House for leaving House Democrats out of final negotiations and agreeing too quickly to a GOP proposal on the estate tax.

According to several Democratic members and aides, much of the discussion focused on the addition of the estate tax provision to the package. The estate tax is scheduled to be reinstated at a higher rate of 55% next year, with the exemption up to $1 million. A bill that passed in the House a year ago set the threshold for the exemption at $3.5 million and the tax rate at 45%, while the provision in the tax deal exempts estates up to $5 million and sets a lower rate.

"My sense is people are not happy with this," said Democratic Rep. Allyson Schwartz of Pennsylvania, who also told reporters that Democrats plan to "push back a little" at the White House to try to change the estate tax back to the version that passed the House. Schwartz said if the administration agreed to do that, she could support the package, but she could not predict how many other Democrats would do the same.

House Majority Leader Steny Hoyer didn't directly answer a query on whether he believed House Democrats could make significant changes to the administration's plan.

CNN's Ed Henry, Deirdre Walsh and John Helton contributed to this report.