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A senior White House adviser held out hope Tuesday that President Obama's jobs bill would attract the "vast majority" of Democrats, even as one leading lawmaker confirmed that Democrats will break up the package that has failed to attract needed bipartisan support.

Sen. Charles Schumer, D-N.Y., confirmed Tuesday that the president's plan will be broken up "piece by piece" despite a Congressional Budget Office report that stated the bill is paid for and would reduce the deficit by $6 billion over 10 years.

Holding out hope early Tuesday, Obama adviser David Plouffe said in interviews that the $447 billion package "should" make it out of the Senate, calling it a "tragedy" if the Senate turns the bill away. The bill is headed for the floor for a vote Tuesday. On NBC's "Today," Plouffe said "there wouldn't be a political issue" if Republicans would just support the proposal.

But even some Democrats have balked at Obama's original plan, with Sens. Joe Manchin of West Virginia, Jon Tester of Montana and Ben Nelson of Nebraska among those leaning toward opposing the legislation Tuesday.

With passage facing long odds, party leaders hope that breaking the legislation into parts will make for greater success in smaller increments. Brendan Buck, spokesman for House Speaker John Boehner, said in a statement that the development was "encouraging."

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"Genius. As you will recall, that was the idea proposed by Republicans nearly four weeks ago," he said.

The details of such a plan are still being worked out. The Wall Street Journal cites one aide as saying Democratic leaders may hold multiple votes on the plan in the coming weeks to underscore Republican opposition.

The idea of tackling the jobs bill in pieces gained the support of Obama last week, when he called in a news conference for Congress to show some progress in acting on his proposals.

The full $447 billion plan to promote job growth is due for a procedural vote Tuesday in the Senate in a slightly different form from what Obama proposed a month ago. In this version, most of the cost would be offset by a surtax on millionaires.

Republicans appear united in opposition and Democrats, with 53 votes in the Senate, face a difficult task in coming up with the 60 votes needed in the 100-member chamber to keep the bill alive.

Obama campaign adviser David Axelrod issued a memo obtained by Fox News that says the majority of Americans support the ideas in the American Jobs Act whereas Republicans offer no alternatives but to reduce the size of government and by extension the investments it can make.

"As members of Congress take up the American Jobs Act this week they need to understand that their failure to focus on what matters most to Americans is why disapproval for Congress is at a historic high – 80 percent ," Axelrod wrote.

But New York tax consultant David Selig said the so-called millionaires tax would fail to achieve its objectives because of multiple tax code offerings that allow high income earners to enter into deferred compensation agreements and other legal tax avoidance schemes. He added that the costs associated with administering the tax would exceed the supposed benefits, including the dedication of the IRS to target the one class of taxpayers

He predicted the immediate projected costs for creating the program would exceed $300 million whereas the revenues can't be determined.

Meanwhile, free trade agreements with South Korea, Colombia and Panama are much more likley to pass Congress. The agreements have been pending since the presidency of George W. Bush. Supporters of the treaties -- the first completed in the Obama administration -- say the pacts could boost exports by $13 billion a year and foster tens of thousands of American jobs.

The House takes up the three agreements on Tuesday, along with legislation pushed by Obama and Democrats to help workers displaced by foreign trade. Both chambers could sign off on the measures by Wednesday night.

The Senate on Tuesday is also expected to pass legislation to impose tariffs on Chinese exports if the Beijing government continues to keep its currency undervalued. Supporters say the measure will make American producers more competitive and bring jobs back home.

The bill enjoys broad bipartisan support from senators who for years have been hearing complaints from constituents blaming unfair competition from China for shuttering U.S. factories and putting Americans out of work.

But the bill faces an uncertain future.

House Speaker John Boehner, a Republican, opposes it and may never bring it to the House floor. Obama and the White House, while avoiding a position on the bill, have warned against unilateral action that might violate international trading rules. American companies doing business in China warn that it could spark a trade war.

But with the trade deficit with China hitting $273 billion last year and heading toward $300 billion this year, senators said it was time to get tough.

"If China continues its predatory practices, the future for our children and grandchildren in this country will not be bright," said Sen. Charles Schumer, a Democrat who has tried numerous times in past years to slap sanctions on the Chinese.

Economists say China's currency, the yuan, is undervalued by about 25 to 30 percent, and possibly by as much as 40 percent against the dollar. That means that Chinese goods sold in the United States have a 25 to 30 percent price advantage, and U.S. goods exported to China face a disadvantage of that same amount.

The Fair Currency Coalition, a group pushing for changes in China's exchange rate, gives the example of a steel mill that might cost 4 billion yuan to build in China. It says that at an equitable currency rate that would mean a price tag of about $900 million, but at current rates it would cost only $600 million, creating a bigger incentive to abandon factories at home and relocate.

The legislation does not specifically mention China but would make it easier for the Treasury Department to declare a currency misalignment. It would require action if the offending country does not address the problem, or allow individual industries to petition the Commerce Department for redress if a competitor nation is using its currency as an export subsidy.

The Associated Press contributed to this report.