(CNN) - Casey Anthony's lawyer said Wednesday that her acquittal signified justice for little Caylee Anthony, who prosecutors unsuccessfully argued died at the hands of her mother.

"Caylee would never have wanted her mother to suffer this way," defense attorney Jose Baez told Barbara Walters of ABC News. "Caylee certainly never wanted her mother to die."

Baez and prosecutor Jeff Ashton separately spoke publicly and with the media Wednesday about their reactions to the verdict.

Confident the state had presented everything it could to prove Casey Anthony killed her daughter, Ashton recalled his shock when Florida jurors decided otherwise.

"When I heard the 'not guilty' on the child abuse, I knew that was it," said the assistant state prosecutor. "I remember mouthing 'wow' four or five times to myself."

Ashton, speaking with InSession's Beth Karas, said he is convinced there was no evidence that Caylee, 2, died accidentally in 2008.

After less than 11 hours of deliberation, a jury Tuesday found Casey Anthony not guilty of first-degree murder and the other most serious charges. But the jury convicted her on four misdemeanor counts of providing false information to law enforcement officers. She will be sentenced Thursday.

Juror Jennifer Ford told ABC News that she and the other jurors cried and were "sick to our stomachs" after voting to acquit Anthony.

"I did not say she was innocent," said Ford, who had previously only been identified as juror number 3. "I just said there was not enough evidence. If you cannot prove what the crime was, you cannot determine what the punishment should be."

Washington (CNN) - President Barack Obama said Wednesday he wants a deal with Congress in the next two weeks to tackle mounting deficits and allow an increase in the federal debt ceiling, but he didn't rule out using a constitutional argument to increase how much money the government can borrow.

"I don't think we should even get to the constitutional issue," Obama said during a Twitter town hall at the White House in response to a tweeted question on whether he would rely on a clause in the Fourteenth Amendment to unilaterally raise the debt ceiling.

The debt ceiling should not be "used as a gun against the heads of the American people to extract tax breaks for corporate jet owners," Obama said, calling for "a balanced approach where everything's on the table."

With congressional leaders heading to the White House on Thursday to continue negotiations, Obama said that people need to "put their dogmas aside" and "their sacred cows aside."

However, Senate Minority Leader Mitch McConnell, who will take part in Thursday's talks, objected to the president's characterization of his side's positions as absolutist or maximalist.

"We have a better term for it - common sense," McConnell, R-Kentucky, said of GOP oppositon to tax increases and more government spending in some areas.

The House returned to work Wednesday from its Fourth of July break, a day after the Senate cut short its recess come back to Washington, with the two parties at sharp odds over what sort of conditions should be attached to a hike in the current $14.3 trillion debt ceiling.

Republicans are refusing to go along with any debt ceiling increase unless it includes deep spending cuts and avoids any tax increases. Democrats are trying to minimize the impact of cuts to social services and are calling for the elimination to certain tax breaks and loopholes benefiting wealthier Americans.

Treasury Department officials and leading economists have warned of potentially catastrophic consequences if the ceiling is not raised by August 2, at which point the country could default on its debt obligations. Among other things, the country could face skyrocketing interest rates and a plummeting dollar.

Increasing the debt ceiling will allow the government to borrow more money in order to pay for spending already accrued.

New York (CNN) - Attorneys for Dominique Strauss-Kahn said Wednesday that the defense team had a "constructive meeting" with prosecutors, who maintain that they are not ready to drop sexual abuse and attempted rape charges against the French financier after questions were raised about the accuser's credibility.

"The investigative process is continuing, and no decisions have been made," said Manhattan District Attorney spokeswoman Erin Duggan.

The two-hour meeting came just days after prosecutors disclosed credibility issues regarding the hotel maid who accused Strauss-Kahn of sexually attacking her.

"We had a constructive meeting today with (Manhattan District Attorney Cyrus Vance) and his colleagues," said a statement from William W. Taylor III and Benjamin Brafman.

Strauss-Kahn pleaded not guilty in June to charges that prompted him to resign from his post as managing director of the International Monetary Fund.

Questions about the case surfaced last week when Vance indicated that the woman, 32, had been less than truthful with authorities about some aspects of her life and her whereabouts immediately after the alleged attack at the Sofitel hotel May 14.

Legal analysts suggest that prosecutors are looking for ways to salvage the case.