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.
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.
Associated Press writers Andrew Taylor, Laurie Kellman, Julie Pace and Alan Fram contributed to this report.
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