Representative John A. Boehner of Ohio, the House Republican leader, used the White House meeting to push for the release of more memorandums documenting the use of the harsh techniques, suggesting they could show that the interrogation methods were effective, as former Vice President Dick Cheney has claimed.

The president did not foreclose the release of more documents, officials briefed on the session said. But Mr. Obama suggested to Mr. Boehner that the additional information would not be definitive on the value of the information obtained from the detainees, they said.

Although a full-scale independent inquiry now appears unlikely anytime soon, the Bush administration’s use of waterboarding and other techniques that critics say crossed the line into torture could still be examined by a variety of Congressional panels in addition to the Senate Intelligence Committee.

Mr. Reid, who repeatedly denounced the use of harsh interrogation techniques when George W. Bush was president, suggested that naming a special panel would signal an intent to exact “retribution,” and he sought to paper over the disagreement with members of his own caucus, like Senator Patrick J. Leahy of Vermont, who have joined human rights groups in demanding a commission.

Mr. Reid said it was premature to act without the facts that will be provided by the Intelligence Committee. “They will make a public report,” he said. “I hope that it will come toward the end of this year.”

But it is actually unclear how much of the panel’s findings will ever be made public. The chairwoman of the committee, Senator Dianne Feinstein of California, has said it is too early to know how much can be reported publicly about an investigation that is dealing largely with classified information.

While the issue is getting less attention, Congress is also showing uncertainty over whether and how to pursue a broad investigation into the causes of the economic crisis. Some lawmakers have argued for a special Congressional committee to handle the inquiry while others want an outside panel with no Congressional ties to take on the job, to avoid any conflicts of interest.