President Bush tried to calm financial markets and American citizens on Friday, saying he expects lawmakers to have plenty of opinions, but Congress will pass a rescue plan for Wall Street.

Meanwhile, Senate Majority Leader Harry Reid said if negotiators can agree to principles of agreement for a bailout, a deal could be done by midnight.

Bush spoke as markets opened more than 100 points down upon news that late-night talks got lawmakers no closer to passing a $700 billion plan to help corporations overburdened with bad mortgage securities. On top of that, federal officials announced that JP Morgan would be buying up Washington Mutual after it suffered the largest failure in U.S. banking history.

"There is no disagreement that something substantial must be done. The legislative process is sometimes not very pretty, but we are going to get a package passed," he said in a brief statement after a long night of difficult negotiations. "We will rise to the occasion."

"My administration continues to work with the Congress on a rescue plan and we need a rescue plan. This is hard work. Our proposal is a big proposal and the reason it's big and substantial is because we have got a big problem," he said.

On Thursday, the president hosted a historic meeting at the White House on the financial crisis. It included not only Hill leaders but presidential nominees John McCain and Barack Obama as well. But the meeting was divisive, and more talks were being held among Banking and Financial Services committee leaders.

Friday, those leaders — Sens. Chris Dodd, D- Conn., and Judd Gregg, N.H., joined House Reps. Barney Frank, D-Mass., and Spencer Bachus, R-Ala. — were expected to reconvene during the day after their staffs developed additional principles of agreement. Treasury Secretary Hank Paulson could be brought in to join them later, when it's clear whether progress is being made.

Frank said any agreement depends on House Republicans "dropping this revolt" against the Bush-requested plan.

Frank said leading Democrats on Capitol Hill were shocked by the level of divisiveness that surfaced at Thursday's extraordinary White House meeting, leaving six days of intensive efforts to agree on a bailout plan in tatters only hours after key congressional players of both parties had declared they were in accord on the outlines of the $700 billion bill.

"We need to get the president to get the Republican House in order," Sen. Charles Schumer, D-N.Y., added while on the Senate floor. "Without Republican cooperation, we cannot pass this bill."

But House Republicans continued to work Friday on an alternative plan that one staffer said they think will work better than the administration's approach. Bachus was also in on those talks, which were led by Minority Leader John Boehner of Ohio.

One staff aide familiar with the talks told FOX Business Network that the White House considered three alternatives: the $700 billion bailout, a private insurance program for mortgage-backed assets and a direct lending/capital infusion program.

They say the White House chose the $700 billion bailout because it thought the plan would have the most upside for taxpayers, once assets are cleaned up and sold.

But House Republicans want a serious consideration of the private insurance plan, and they expect to have draft legislation ready by this weekend. They are also reaching out to Democrats to see if there could be bipartisan support for this alternative.

Many House Republicans do not want the government involved in this or taxpayer money used for it. The aide stressed that everyone in the group is of the mind that something has to be done to stabilize financial markets and they want some plan — just not the Paulson plan.

The mortgage insurance security fund is the cornerstone of their alterative, and bill language on that is coming along. The idea is to collect fees for premiums to insure the mortgages companies guarantee. If a mortgage goes into default, the fund would pay it off for the investor/holder.

According to a separate source, the logic is that the federal government has insured approximately half of all mortgage-backed securities through its sponsorship of mortgage lenders Fannie Mae and Freddie Mac. Sources said the understanding is that a private fund could work because capital is available, it's confidence that is lacking, but if the U.S. government backs the fund, it will allow private capital to return to the market.

The group is waiting on legislative language from the Congressional Budget Office to see how much it will cost, but members expect it to be substantially less than $700 billion, the staff aide said.

The source said the biggest misconception about the existing plan is that it had the votes from both sides to actually make it through Congress. The fact of the matter is, the Democrats did not back Paulson's plan, and offered another option that looked like it.

The GOP proposal is aimed at opening up talks that Democrats had shut down. The House GOP caucus was expected to meet later in the day.

In a letter to House Speaker Nancy Pelosi, Boehner suggested that the Democrats have tried to cast the breakdown in communications as the fault of the Republicans, which he said was unfair and incorrect.

"Over the last week, we have frequently discussed Secretary Paulsons proposal, and I have repeatedly expressed the need for improvements on behalf of myself and my Republican colleagues," he wrote.

"Yet Chairman Frank and Chairman Dodd, on several occasions over the last several days, announced that a bipartisan deal was at hand even though the reservations about the underlying proposal I had expressed to you had not been addressed," Boehner continued. "Madam Speaker, we owe it to all those with a stake in this process to continue our discussions until we arrive at an agreement that is acceptable on both sides of the aisle — and more importantly, one that serves the interests of American taxpayers."

Reid said that he thought the insurance idea was a no-go.

"Secretary Paulson has said their insurance programs won't work. Whether he will say that publicly, I don't know," he said.

McCain, in the meantime, continues to meet with lawmakers. Early in the morning he held talks with Boehner and other GOP leaders: Minority Whip Roy Blunt, Deputy Whip Eric Cantor and House Republican Conference Chairman Adam Putnam.

Nancy Pfotenhauer, a McCain adviser, said the Republican presidential candidate is "cautiously optimistic that we can all come together around more than just principles."

Pfotenhauer said part of the problem in talks up to now is that "too few people (were) talking about a plan that had not enough detail." She would not say whether McCain was on board with the Republican alternative.

Schumer said Bush should "respectfully tell Senator McCain to get out of town. He is not helping, he is harming. Before Senator McCain made his announcement, we were making progress."

But Pfotenhauer said McCain "is not involved in any grandstanding ... he's listening trying to find areas of agreement and how to craft" a plan that will work for the majority of lawmakers.

FOX Business Network's Peter Barnes and The Associated Press contributed to this report.