It involves substantive issues such as CIA spying on Congress and the power of the legislative branch to oversee the executive branch.
At the core, the matter focuses on how much history to reveal about the way America detained and interrogated terror suspects in response to the 9/11 al Qaeda attacks.
Here are answers to some of the basic questions about the dispute:
1) What is all the yelling about?
More than five years after President Barack Obama ended the controversial interrogation program started during the George W. Bush administration, security chiefs and politicians are still battling over how much official information should be made public.
A 6,300-page report on the program by the Senate Intelligence Committee remains classified amid discussions between Congress and the spy agency on what to reveal.
When researching the report, committee staffers got hold of a separate, internal CIA review of the information made available to Senate investigators.
Alarmed by outside access to the secret document, the CIA then searched computers used by committee staffers and then sought a Justice Department investigation.
On Tuesday, Intelligence Committee Chairman Dianne Feinstein of California publicly accused the CIA of effectively spying on the committee and raised the possibility that the agency impeded the probe and perhaps broke laws in the process.
CIA Director John Brennan responded with a flat-out denial of any wrongdoing.
2) What's really going on?
This is Washington, so there must be a political angle, though other considerations also come into play.
For example, participants in the detention/interrogation program could face lawsuits at home and abroad over their role in torture such as waterboarding.
Some cases are pending and rights groups continue to press for more information for possible further challenges by current and former detainees.
In comments Tuesday to the Council on Foreign Relations, Brennan cited the importance of getting the report right, saying Americans "owe it to the women and men who faithfully did their duty in executing this program to try to make sure that any historical record of it is a balanced and accurate one."
"I will protect sources and methods, you know, in terms of the tremendous investment that this country has made in some of, you know, the very sensitive collection systems that help to keep this country safe," he said.
The purely political explanation has Democrats seeking full exposure of the Republican roots of the detention and interrogation program described by Feinstein as "un-American" and "brutal."
She described how the committee's investigation that started in full force in 2009 followed revelations that "the interrogations and the conditions of confinement at the CIA detentions sites were far different and far more harsh than the way the CIA had described them to us."
3) Who spied on who?
Spies spy, especially when they think they're being spied on.
Brennan informed Feinstein in January the CIA had looked at the computers used by Intelligence Committee staff to figure out how they got hold of the internal review ordered by former CIA Director Leon Panetta.
"The CIA's search may well have violated the separation of powers principle embodied in the United States Constitution, including the speech and debate clause," Feinstein said Tuesday. "It may have undermined the constitutional framework essential to effective congressional oversight of intelligence activities or any other government function."
However, the CIA has asked the Justice Department to look into whether committee staffers did anything wrong in accessing the so-called Panetta review, which was supposed to be an internal deliberative document and therefore unavailable.
Feinstein insisted her committee workers simply used the access provided them by the CIA, and she called the agency's tactics and response an attempt at intimidation.
"I have asked for an apology and a recognition that this CIA search of computers used by its oversight committee was inappropriate," she said. "I have received neither."
4) What happens now?
More accusations, counter-claims and political wrangling as both sides seek some kind of agreement on what parts of the committee's report can be made public.
While legal ramifications including criminal charges are possible, the back-and-forth so far appears to be more about pressure tactics and brinksmanship.
Republicans have kept mostly silent about the dispute, though Rep. Mike Rogers of Michigan, who chairs the House Intelligence Committee, told CNN that any wrongdoing should be punished if proven.
Brennan said he's awaiting a request from Congress to declassify portions of the committee report.
Asked about the issue on Wednesday, Obama told reporters that he's "committed to declassifying" the information once the report is completed.
However, Obama said he would not weigh in on the explosive accusation that the CIA overreached and spied on the Senate.
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