NEW YORK (CNNMoney.com) -- The Senate plans to vote on the $700 billion bank rescue plan Wednesday evening - two days after the House failed to pass it.

The bill adds new provisions - including raising the FDIC insurance cap to $250,000 from $100,000 - and will be attached to an existing tax bill that the House also rejected Monday, according to several Democratic leadership aides.

The vote is scheduled for after sundown, in observance of Rosh Hashanah. Republican presidential nominee John McCain, R-Ariz., and Democratic nominee Barack Obama, D-Ill., and his running mate Joe Biden, D-Del., confirmed that they would be present for the vote.

Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., announced the plan Tuesday night.

"Senate Democrats and Republicans believe it is essential that we work quickly on this important legislation to restore confidence to our financial system and strengthen the economy," Reid said in a statement.

White House spokesman Tony Fratto said the administration welcomes the "modified bill" and the scheduled vote.

Democratic sources told CNN that they expect bipartisan support in the Senate.

Tuesday afternoon, Federal Deposit Insurance Corp. Chairman Sheila Bair asked Congress to allow her agency to increase the $100,000 limit per account that has been in place since 1980. To do so would help restore confidence in the markets, she said. Bair did not say what she thinks the new limit should be.

The revised bill contains provisions that the Senate hopes will appeal to House Republicans, who voted two-to-one against the original legislation. The sweeteners include renewable energy tax incentives - for individuals and businesses alike - that have been on the table for several months and had a chance of passing at some point anyway.

The bill also includes relief from the Alternative Minimum Tax, without which millions of Americans would have to pay the so-called "wealth tax."

The debate over extending AMT relief is an annual political ritual. It enjoys bipartisan support but deficit hawks on both sides of the aisle contend the cost of providing that relief should be paid for. Others argue it shouldn't be paid for because the AMT was never intended to hit the people the relief provisions would protect. Nevertheless, lawmakers pass the measure every year or two.

The revised bailout bill also includes a "Mental Health Parity" provision, which would require health insurance companies to cover mental illness at parity with physical illness.

House Speaker Nancy Pelosi, D-Calif., said that House leaders are discussing ideas offered by other lawmakers about how to modify the bill defeated on Monday. "House Democrats remain strongly committed to a comprehensive bill that stabilizes the financial markets, restores confidence, and protects taxpayers," she said.

House Minority Leader John Boehner, R-Ohio, was consulted on the Senate's plans and gave his "green light," Boehner spokesman Kevin Smith said.

"We believe we'll have a better chance to pass this bill than the one that failed [Monday]," Smith added.

However, one aide in the GOP Senate leadership said swaying House Democrats to get on board with the sweetened bill will be "a fairly substantial problem."

The plan could attract Republicans in the House while simultaneously alienating bailout supporters among the Democrats because the tax cuts in the revenue bill aren't offset by spending cuts or increased revenues.

"I am talking with my House colleagues about the Senate action and how to best proceed taking that into consideration in determining what action in the House will be most successful," said House Majority Leader Steny Hoyer, D-Maryland.

Round 1 failed

The bailout package, a collaboration of Treasury Secretary Henry Paulson and leaders from both parties, was rejected by the House in a 228-205 vote Monday. Two-thirds of Republicans and about one-third of Democrats voted against the bill.

Following the defeat, the Dow Jones industrial average dropped 777 points, its biggest one-day point decline ever. The decline of nearly 7% was the largest one-day percentage decline since Sept. 17, 2001, the first day the markets reopened after the Sept. 11 attacks. (See correction.)

But stocks rallied Tuesday, with the Dow jumping 485 points on bets that Congress will pass a version of the government's $700 billion package.

The bill, if approved, would allow the federal government to buy troubled mortgage-related investments from financial institutions, freeing them up for lending in a bid to pull the economy out of its credit freeze.

Proponents of the bill believe it would prevent the United States from sliding into a serious financial crisis, but opponents saw it as an unbearable burden to taxpayers and a rescue for Wall Street.

The Bush administration and key lawmakers had regrouped on Tuesday and vowed to push ahead. "Unfortunately, the measure was defeated by a narrow margin," President Bush said in a brief televised address at the White House. "I'm disappointed by the outcome, but I assure our citizens, and citizens around the world, that this is not the end of the legislative process."

The House is adjourned and not scheduled to return to session until Thursday at noon.

Bush pushed hard for lawmakers to act. "Our economy is depending on decisive action from the government," he said. "The sooner we address the problem, the sooner we can get back on the path of growth and job creation. This is what elected leaders owe the American people, and I am confident that we'll deliver."

On Tuesday, Bush also spoke to Obama and McCain about the financial crisis, according to Fratto. The presidential candidates "offered ideas and reaffirmed what they have said publicly - that this is a critical issue that needs to be addressed," Fratto said.

CNN's Jessica Yellin, Deirdre Walsh and Ted Barrett contributed to this story.

Correction: An earlier version of this story incorrectly stated the 7% drop in the Dow on Monday was the second biggest one-day decline since Black Monday in 1987, when the Dow dropped 22%.