President Barack Obama’s first-ever use of executive privilege to block a congressional investigation is a reminder of the uncertain dividing line between congressional and executive branch authority — and the even murkier legal process for deciding who wins the upper hand in such fights.

In a letter to Obama on Tuesday, Attorney General Eric Holder said the documents a House committee is seeking about the Justice Department’s response to Operation Fast and Furious “fit squarely within the scope of executive privilege.”

Republicans called the privilege claim frivolous, particularly since the documents don’t appear to involve White House officials or presidential decision making.

“The assertion is transparently invalid in that it is not credible that every document withheld involves a communication authored or solicited and received by those members of an immediate White House adviser’s staff,” Rep. Trey Gowdy (R-S.C.) said in an amendment offered during the House Oversight and Government Reform Committee session, during which members voted along party lines to recommend holding Holder in contempt of Congress.

Sen. Chuck Grassley (R-Iowa) said in a statement that Obama’s action “raises monumental questions,” including: “”How can the president assert executive privilege if there was not White House involvement?”

Legal experts say the question of how far executive privilege extends down into the executive branch has never been definitively resolved by the courts.

“There isn’t a lot of law on it,” said Stan Brand, a former House counsel now in private practice. “It’s each side brandishing their own internal opinions, which aren’t ratified by any court.”

The privilege’s scope when Congress is the party seeking information is particularly uncertain.

“On the congressional side, … nobody can say what the rules are with much definiteness,” said Neil Eggleston, a lawyer who defended the Clinton White House in several privilege fights.

The existence of a privilege to keep White House communications confidential under most circumstances is well established. Some presidents, like Richard Nixon, suggested that the privilege should extend to virtually everyone in the executive branch, but legal scholars have been skeptical of that since it could render almost the entire government immune to routine congressional oversight.

“Nixon got in trouble for saying that members of the executive branch are an extension of the president himself. … That was a huge stretch,” said Mark Rozell, a professor of public policy at George Mason University and author of a book on executive privilege. “This principle has been established as distinctly a presidential power. … It belongs to him and certain high-ranking officials in the White House who may be privy to internal deliberations. It’s not this broad-based principle that applies to the executive branch all the way down to the middle and lower levels.”

However, one lawyer who has generally defended congressional demands for executive branch information said the communications in dispute now — involving how Holder and his top aides responded to the congressional probe into Fast and Furious — may well be covered by the privilege.

“While often that’s questioned if you push it all the way down the civil service, here we’re talking about the level of the attorney general and the assistant attorney general for legislative affairs and that’s not so far down,” said Charles Tiefer, a former acting House counsel and a law professor at the University of Baltimore. “These are not low-ranking offices.”

Tiefer said Obama’s assertion was “a fair claim, but still not as strong a claim as deliberations at the White House level.”

Another key question regarding Obama’s privilege claim is just what can Congress do to fight it?

Brand said the process of holding the attorney general in contempt grabs headlines but its immediate practical consequences for Holder and the administration are minimal.