Investors around the world were less on edge Sunday after President Barack Obama said an agreement had been reached to raise the federal government's borrowing limit and avoid a possible U.S. debt default.

Japan's benchmark Nikkei index was the first major stock market to open for trading at 6 p.m. Mountain time on Sunday. After Obama's televised statement, the Nikkei was up 1.7 percent.

There's also evidence that investors believe the deal Obama announced is likely to pass in Congress.

After the deal was announced to raise the debt limit and cut at least $1 trillion in spending over the next decade, Dow futures were up 182 points, or 1.5 percent. Future contracts for the broader S&P 500 index rose 1.6 percent. When futures are up during off-hours trading, stocks typically rise when the market opens.

If the deal is approved, John Brady, a senior vice president for futures and options at MF Global believes "stocks will rally, and stocks will rally big."

He said Monday could be an up and down day for markets. Stocks will rise if the news out of Washington is that the deal is on track and will fall if news leaks that the deal might be in trouble. If the deal fails to pass in Congress, he said: "The rally will be torpedoed."

Jack Ablin, chief investment officer at Harris Private Bank in Chicago, said the agreement could lead to a rally even before a vote in the House or Senate.

"I think this spells relief on Wall Street," he said shortly after the accord was announced and congressional leaders endorsed it.

A deal would remove a major source of something investors hate: Uncertainty. But there's another reason a so-called relief rally might be a big one. Companies have reported strong quarterly earnings in the past few weeks. But traders have been reluctant to buy stocks on the good news fearing the debt wrangling in Washington might set off a financial crisis.

Thomas Tzitzouris, head of fixed income research at Strategas Research Partners said Sunday that to avoid a steep decline, the market needs to believe there is progress toward the deal.

If not, he said: "When (Congress says) there is progress and then there isn't, that really spooks the market. That would be a double whammy.

That's what happened last week when a series of proposals gave investors hope there would be a deal. But one party shot each one down. Nearly every measure of market confidence fell last week as Tuesday approached without a deal. Gold, which tends to rise when investors aren't confident about other investments, rose 2 percent last week. A measure of stock market volatility, the VIX, jumped 6 percent.

In turn, the yield on the 10-year Treasury note sank to its lowest level of the year on Friday, 2.80 percent. Treasury yields fall when demand for them goes up. And demand tends to rise when investors are worried and want a safe place to put their money. Treasury bonds have long been considered the world's safest investment and are a top holding of the largest pension funds in the U.S., millions of Americans who own mutual funds and many foreign governments.

If the agreement to raise the nation's borrowing limit and defuse the building financial crisis does not pass in both the House of Representatives and the Senate, analysts said Sunday that they expect stock markets across the globe to fall on Monday.

In the U.S. that would add to six straight days of stock losses. The Dow Jones industrial average fell 581 points, or 4.6 percent, in that time.

Brady predicts the S&P 500 could fall as low as 1,200 in the next two days if there is no deal before the market opens Monday. That would be a 7 percent drop from Friday's close of 1,292 on Friday. The S&P was down 3.9 percent last week. A loss of another 7 percent would send the S&P down to a level it hasn't reached since last November.

The Treasury Department has said that after Tuesday the U.S. government won't have enough money to meet all of its financial obligations if Congress doesn't raise the nation's debt ceiling. If a deal isn't approved, the Treasury Department will have to decide which bills to pay and which to delay.