The $827 billion Senate version of the plan - designed to bring the economy out of the worst downward spiral since the Great Depression of the 1930s - was expected to pass the upper chamber Tuesday. The House of Representatives has already passed its $820 billion version of the measure.
Negotiators from both chambers were likely to begin reconciling differences between the two versions later this week, with Obama still pressing to have the stimulus measure on his desk for signing by mid-month.
In addition to the $40 billion in aid to state and local governments, the House version has $2.6 billion for a first time home buyer tax credit, but there's an income cap, reports CBS News correspondent Kimberly Dozier. The Senate's has $18.5 billion to give a credit to any homebuyer, no matter how much they earn.
And the Senate bill includes $70 billion to protect middle class Americans from paying the much-hated Alternative Minimum Tax. The House bill doesn't have that, Dozier reports.
But without the infusion of federal money to state and local governments, the country may still face "a vicious cycle of layoffs, falling home values, lower property taxes, more layoffs," Lawrence Summers, chairman of the White House National Economic Council, said.
A key leader in the House, Rep. Barney Frank, chairman of the House Financial Services Committee, added weight to Summers' comments, chiding Republicans for ignoring the outcome of the November election.
"We had an election last year which had pretty decisive results in the White House, the Senate and the House," the Massachusetts Democrat said. "And it did say that public spending for improved infrastructure, to keep bridges from crumbling, to keep cops and firefighters working is a good thing."
The Senate measure was pared back from more than $900 billion to entice a handful of necessary votes from Republican moderates in support of the legislation. The House bill passed without a single Republican "yes" vote, a huge slap to Obama's vows to take the debilitating partisan heat out of Washington politics.
Republican Sen. John Cornyn of Texas said, meanwhile, that he expected the stimulus package to pass the Senate, but he warned that it could damage the U.S. economy in the future.
A stark critic of Obama's approach to righting the badly damaged economy, Cornyn said he believes passage of the $800-plus billion measure with minimal Republican support must be a major disappointment to Obama.
The Texas Republican argued that the stimulus package is loaded down with pet Democratic spending projects and is, in Cornyn's words, "just spending as far as the eye can see."
Sen. John Ensign, a Nevada Republican, rejected Democratic criticism that his fellow Repubicans were dragging out passage of the bill.
"It'll pass this week, but we want some time to go through it, we want some time for the American people to be able to look at it," he said.
Republicans claim that Democrats have failed to learn the lessons of history, arguing that an Obama-style stimulus did not really work in the 1930s, when last tried by former President Franklin D. Roosevelt who took over the White House facing similar economic upheaval.
Summers was blunt in rejecting the criticism.
"Those who presided over the last eight years, eight years that brought us to the point where we inherited trillions of dollars in deficits, an economy that's collapsing more rapidly that in any time in the last 50 years, don't seem to be in a strong position to lecture about the lessons of history," he said. "We need an approach that's very different from the approach that brought us to this point."
Summers appeared Sunday on ABC television's "This Week" and "Fox News Sunday" while Cornyn appeared on the Fox program. Frank and Ensign spoke on NBC's "Meet the Press."
Given broad public support in the first three weeks of his presidency, Obama has found himself playing defense over the stimulus plan. Republicans picked the measure apart in both houses of Congress, focusing on portions of it that run counter to the opposition party's philosophical core - small government and lower taxes.
The Republicans accuse Democratic colleagues of loading the measure down with unneeded spending projects that do not stimulate the economy that is tumbling into the worst swoon in eight decades.
As he tries to regain the upper hand, Obama will take his case to the American people this week with his first prime-time news conference on Monday. He also plans to participate in town hall-style meetings in cities suffering particularly hard times - Elkhart, Indiana, on Monday and Fort Myers, Florida, on Tuesday.
Obama's news conference was initially scheduled to follow Treasury Secretary Timothy Geithner's announcement of the administration's new framework to aid the financial sector.
But Geithner's announcement was pushed back to Tuesday because the administration wants to spend the day focused on the Senate's effort to pass the economic recovery package, Treasury spokesman Isaac Baker said.
The financial plan that Geithner is expected to detail will spell out how the administration intends to loosen credit by using the unspent money in a $700 billion bailout fund approved last fall for banks and other financial institutions.
Things have not gone quite the way the new Obama team expected in getting the massive stimulus package through Congress. It has been a rough two weeks of on-the-job training for the former one-term Illinois senator.
"You know, it's referred to as sausage-making and probably for good reason," said White House spokesman Robert Gibbs, referring to the legislative process.
Among the most difficult cuts for the White House and its liberal allies to accept in the Senate bill was the elimination of $40 billion in aid to states, money that economists say is a relatively efficient way to pump up the economy by preventing layoffs, cuts in services or tax increases.
Still, Obama aides claimed they were satisfied with the results, given the enormity of the challenge. "In a matter of weeks, we moved through both houses of Congress a very complex piece of legislation," Obama senior adviser David Axelrod said Saturday in an interview. "I don't know if there is a parallel in history."
"We can't afford to make perfect the enemy of the absolutely necessary," Obama said Saturday in his weekly radio and Internet address, sounding a note of pragmatism that liberal followers rarely heard on the campaign trail.
Still, the popular president scolded Republicans with a pointed reminder that Democrats, not Republicans, were victorious in November.
Hours later, the Senate convened a rare Saturday session to debate a compromise forged between Republican moderates and the White House on Friday, a rare burst of comity aimed at securing passage of the bill with a few Republican votes joining the Democratic majority.
The compromise reached between Republican moderates led by Sen. Susan Collins of Maine, the White House and its Democratic Senate allies stripped $108 billion in spending from Obama's plan.
While cutting out projects that likely would give the economy a quick lift, the Senate measure retained items that probably won't help the economy much, such as $650 million to help people without cable receive digital signals through their old-fashioned televisions or $1 billion to fix problems with the 2010 Census.
The bill, nevertheless, retains the core of Obama's plan, designed to ease the worst economic recession in generations by combining hundreds of billions of dollars in spending to boost consumption by the public sector with tax cuts designed to increase consumer spending.
Much of the new spending would be for victims of the recession, in the form of extending unemployment insurance through the end of the year and increasing benefits by $25 a week, free or subsidized health care, and increased food stamp payments.