They are also watching signals from the U.K., where Cameron has said he would leave the formal triggering of the split to his successor, who is not expected to be in place until September. That trigger is known as Article 50, and the leaders of Germany, France and Italy said on Monday that there could be no negotiations with Britain on its departure until it formally invoked the article.
U.S. data Tuesday includes the third look at first-quarter GDP, expected to rise to 1 percent. It is released at 8:30 a.m. EDT. There are also S&P/Case Shiller home prices and consumer confidence, at 10 a.m. EDT.
The Brexit vote wreaked havoc on markets for a second day Monday, and the S&P 500 sank to the key 2,000 level, off 1.8 percent. Treasury yields fell again, with the U.S. 10-year at 1.43 percent late Monday afternoon. The U.K. pound continued to drop, falling as low as 1.31, a decline of about 3.5 percent against the dollar.
"I think it's going to be with us for a while. The economic data matters, but what matters more is what does [German Chancellor Angela] Merkel say; what does Cameron say and what does Boris Johnson say? Who knows? These are politicians. How do you discount that in the market?…How do you value what they're going to say and how do you judge when they're going to say something?" said Jim Caron, fixed income portfolio manager at Morgan Stanley Investment Management.
Boris Johnson, the former Mayor of London and a key leader of the leave movement, is a possible candidate to replace Cameron. But he has muddied the situation even further by saying that Britain should take its time before moving to separate from the EU, and that the U.K. could still be in a trading bloc with Europe.
"It became very obvious from watching interviews and reading comments this weekend that the leave camp did not expect to win and has absolutely no game plan whatsoever. From where I sit, I am clueless, and I'm not sure sitting close to it would give you any more clues," said Ward McCarthy, chief financial economist at Jefferies.
The confusion inside Britain's political parties has fed the uncertainty that's disturbing markets. Brown Brothers Harriman's chief currency strategist Marc Chandler noted that sterling could lose as much as 20 percent from its pre-vote 1.50 to the dollar.
"We anticipated a 15-20 percent slide in sterling. From the $1.50 level that would target $1.2750 (15 percent) and $1.2000 (20 percent), which still seems reasonable," he wrote.
As for the politicians, "The only thing that seems to compare with the Tory Party's seeming cluelessness on how to proceed is the disarray of the Labour Party," Chandler wrote.
"The 229 Labour MPs will have a confidence vote on their leader (Jeremy) Corbyn. The results will likely be known toward the end of the business day in London Tuesday. The vote is advisory in nature, but the more that vote against Corbyn, of course, the more precarious his position."
Corbyn is under fire for the failure of the remain campaign effort.