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 8 p.m. Eastern 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 today 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.

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.