WASHINGTON — The Senate today overwhelmingly passed a sweeping tax package that would save millions of Americans thousands of dollars in higher taxes while also reducing their Social Security taxes and extending jobless benefits.

President Barack Obama swiftly urged the House to pass the $858 billion bill without changes, a slap at Democratic liberals eager to toughen a part of the measure that permits up to $10 million to pass to heirs estate tax-free.

A wide array of tax cuts enacted under President George W. Bush is scheduled to expire on Jan. 1 — just two weeks away — affecting taxpayers at every income level. The bill passed by the Senate, 81-19, would extend those cuts for two years.

Obama urged quick action in the House.

“I know there are different aspects of this plan to which members of Congress on both sides of the aisle object. That’s the nature of compromise,” the president said. “But we worked to negotiate an agreement that’s a win for middle-class families and a win for our economy, and we can’t afford to let it fall victim to either delay or defeat.”

House Democratic leaders said they expect to vote on the bill Thursday.

Obama negotiated the package with Senate Republicans, and then administration officials worked for days to persuade congressional Democrats to support it, signaling a possible blueprint for future legislation. Because of November’s election victories, Republicans will take control of the House in January and gain seats in the Senate.