WASHINGTON — Senate Democrats are rewriting portions of President Barack Obama’s jobs bill to include a new 5 percent tax on income above $1 million — a proposal that is sure to be blocked by Republicans.

Senate Majority Leader Harry Reid, D-Nev., said today he is changing the plan in an effort to attract more votes from fellow Democrats. He said he plans to bring the bill to the floor next week. Reid, however, wouldn’t predict whether Democratic senators would unite behind the measure, which is unlikely to get any support from Republicans.

The new tax would replace tax increases sought by the president. Obama’s plan called for raising taxes by limiting itemized deductions — including those for charitable donations and mortgage interest — for individuals making more than $200,000 and married couples making more than $250,000.

Reid said the millionaire’s tax would cover the entire cost of Obama’s jobs bill — about $450 billion over the next decade.

Sen. Chuck Schumer, D-N.Y., said there was opposition to Obama’s plan because people making $250,000 or $300,000 in high cost areas, like New York, don’t consider themselves rich.

“Drawing a line at $1 million is the right thing to do,” Schumer said.

The top income tax rate is currently 35 percent, on taxable income above $379,150. Under the bill, the new top rate for millionaires would go to 40 percent.

Reid announced plans to move the bill as Obama tried to blame Republicans for Congress’ failure to act.

Obama traveled to Texas Tuesday 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.

Cantor has said the White House’s “all or nothing approach is unreasonable.”

But 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.

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,” Sen. Joe Manchin, D-W.Va., said of the bill’s price tag.

Democrats said Reid’s proposed millionaires’ surtax was designed to quell much if not all of the opposition from his own rank and file.

To pay for his package of tax breaks, unemployment benefits and new spending on public works projects, 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, but those increases, too, would disappear under the changes Reid outlined today.

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 themselves open to a charge of protecting the wealthy at the expense of the unemployed.

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