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Senate Democrats are considering a surtax on millionaires to offset the cost of President Barack Obama's $445 billion jobs bill, according to several party aides.

Senate Majority Leader Harry Reid, D-Nev., outlined plans for a 5 percent surcharge in a closed-door meeting with the rank and file, according to participants, as Obama traveled to Texas to deliver his most caustic challenge yet to House Republicans who have not allowed a vote on the legislation unveiled nearly a month ago.

"What's the problem? Do they not have the time? They just had a week off. Is it inconvenient?" he said in Mesquite, Texas, singling out House Majority Leader Eric Cantor for special criticism.

There was no indication Cantor, R-Va., or the House Republicans would agree.

The move would be an effort to win more support for the package within the Democratic Party. Republicans have said they oppose the plan, and even some Senate Democrats have been critical of aspects of the plan.

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After three weeks of presidential demands for Congress to pass his jobs bill without delay, White House communications director Dan Pfeiffer said Obama was open to Reid's changes.

"We offered a balanced way to pay for the American Jobs Act, but if Congress has a better idea that ensures that everyone pays their fair share, we're open to it," Pfeiffer said.

On a day rich in political maneuvering, Senate GOP leader Mitch McConnell announced he was ready for an immediate vote on the bill, even though he opposes it. Reading aloud on the Senate floor from a copy of Obama's speech, he said, "I do think the president makes an important point that he is entitled to a vote."

The request was blocked by Reid, who called it a "political stunt" and said he would make sure the bill comes to the floor this month. Aboard Air Force One, White House press secretary Jay Carney accused Republicans of gamesmanship.

The parliamentary dance aside, the day's events underscored that as submitted by the White House, Obama's bill would not only fail in the Republican-controlled House, but faced enough opposition from Democrats to endanger its prospects in the Senate, as well.

"There's the good, the bad and the ugly. The ugly was $447 billion," said Sen. Joe Manchin, D-W.Va., referring to the overall size of the president's request.

Yet while Republicans and Democrats appear to be pointing to a showdown that could reverberate into the 2012 election campaign, some elements of the measure could clear Congress with relative ease by year's end.

As an example, Republicans have not ruled out extending and expanding the payroll tax cuts that took effect on Jan. 1, at a cost of $247 billion over a decade, the single priciest item in Obama's legislation.

Democrats said Reid's proposed millionaires' surtax was designed to quell much if not all of the opposition from his own rank and file, a subject that Sen. Dick Durbin of Illinois, the second-ranking leader, referred to in an interview with reporters.

"We're also obviously going to work on the number of votes to support it. It may not be the exact plan offered by the president, but I think he, when he presented it to us, said that we need to be open to some variations and modifications," Durbin said.

The payroll tax cut extension faces little if any opposition from Democrats, and Obama's request for more than $100 billion in new spending as a way of creating jobs is also popular within his own party.

To pay for his $447 billion plan, Obama has proposed higher taxes on family incomes over $250,000 and on the oil and gas industry.

The first request troubles Democratic senators from states like New York, New Jersey and California, where large numbers of families could be hit by the increase. The second has drawn opposition most prominently from Louisiana Sen. Mary Landrieu, whose state is home to numerous oil and gas operations.

The president also proposed higher taxes on hedge fund managers and corporate jet owners, and those increases, too, would disappear under the changes Reid is expected to unveil as early as Wednesday.

His office declined comment on the emerging plan for a surcharge on millionaires, but several Democrats, speaking anonymously to discuss the developments, said it was being drafted to cover the entire $447 billion cost of the legislation.

In political terms, Democrats appear to be hoping that Republicans will oppose both the higher taxes on million-dollar-earners and the president's call for new spending aimed at reducing joblessness, thus leaving the GOP open to a charge of protecting the wealthy at the expense of the unemployed.

Reid predicted that by the time the jobs bill comes to the Senate floor, almost all Democrats would be behind it. "There could be -- I don't know who -- but there could be some that don't support it. But it would be a rare situation," he added.

In his speech in Texas, Obama referred to Cantor one day after the Virginia Republican said the White House's "all or nothing approach is unreasonable."

"Eric Cantor said that right now, he won't even let this jobs bill have a vote in the House of Representatives. That's what he said. Won't even let it be debated," the president said.

"At least put this jobs bill up for a vote so that the entire country knows exactly where members of Congress stand," Obama said. "Put your cards on the table."

Cantor's spokesman rejected the criticism.

"If House Republicans sent our plan for America's job creators to the president, would he promise not to veto it in its entirety? Would he travel district to district and explain why he'd block such common-sense ideas to create jobs?" Brad Dayspring said. "House Republicans have different ideas on how to grow the economy and create jobs, but that shouldn't prevent us from trying to find areas of common ground with the president."

House Republicans have begun passing legislation to block or roll back administration regulations on several industries, saying their removal will create jobs.

While Republican lawmakers appear receptive to tax cuts the president has called for, they have expressed strong opposition to his proposed new spending.

The Associated Press contributed to this report.