Originally Published: 20 OCT 21 05:05 ET

Updated: 20 OCT 21 08:23 ET

By Tierney Sneed, CNN

(CNN) -- The next few weeks will be pivotal if former President Donald Trump is hoping to bury the House's request for January 6 documents in years of litigation.

With a lawsuit filed Monday, Trump began in earnest his legal war against the House's Capitol insurrection investigation. He is seeking to block the National Archives from releasing the documents to the House select committee investigating the attack.

According to the court filings, Trump has less than a month to get an initial court order blocking the release of the records. The National Archives told Trump last week that it intended to turn over the documents on November 12, as President Joe Biden had declined to assert executive privilege over them.

Trump's efforts to act quickly now to stop the release could ultimately turn into larger strategy to run down the clock, legal experts told CNN. With Democrats in danger of losing control of Congress in next year's midterms, if Trump can drag out the litigation long enough, it could be enough to sink their request for the documents, regardless of how the legal questions are ultimately settled.

If Trump does secure a temporary court order -- a request he's likely to take to the Supreme Court if need be -- blocking the November 12 release, the pace of the proceedings could slow down quite a bit. At least some of the legal ground the lawsuit is seeking to explore is unsettled and could prompt courts to give the questions deliberate review.

"In some ways, it really works in President Trump's favor, because there are so many questions that courts will have to address for the first time," said Emily Berman, a professor at the University of Houston Law Center.

Why Trump must act quickly if he wants drag things out

The case bears some similarity to Trump v. Mazars, the lawsuit that the then-President brought against his accounting firm to stop it from releasing his financial records to the House. While the Supreme Court rejected his most aggressive claims in that case, it punted in a way that has continued to stall Congress' efforts to obtain the documents.

It seems likely that Trump will again push the lawsuit all the way to the Supreme Court if need be, where he will be met by a conservative 6-3 majority. How quickly the Supreme Court is put in the hot seat will depend on the lower courts' handling of the case.

Unlike some of the other litigation that surrounded Congress' investigations into Trump while he was President, the burden is now on Trump to get a court order blocking the document release -- and to get one quickly.

"The posture of this particular suits makes it possible that this could move much faster than say, like the McGahn litigation," said Jonathan Shaub, a former attorney at the Justice Department's Office of Legal Counsel and now an assistant professor at University of Kentucky College of Law. In that case, the House was suing to force Trump White House counsel Don McGahn to appear for testimony. In this case, the Archives has indicated it plans to hand over the documents, so the onus is on Trump to get a court intervention to stop it.

His first stop will be Judge Tanya Chutkan, an Obama-appointee who was not involved in the major Trump oversight cases of the last administration.

"She is a very efficient judge and I suspect will move on this very quickly," Neil Eggleston, a former White House counsel for President Barack Obama, told CNN.

If she declines the preliminary injunction request, Trump will then be relying on the DC US Circuit Court of Appeals, where a panel of three judges would be next to review the case. While the DC Circuit as a whole isn't friendly territory for Trump, in the past he has drawn panel selections that have broken in his favor. After the appeals court panel weighs in, there are a couple of options for either side if they want to keep the battle at the appellate level. The Supreme Court will be Trump's next stop if he is unable to get the immediate intervention he wants at the district or appellate level.

A request to that the Supreme Court block the November 12 release would first be filed on the court's emergency docket -- known informally as its shadow dockets -- though the high court will have a number of options for how quickly or slowly it would want to take its next steps in the case.

If the Supreme Court wanted to, it could fast track a consideration of the case on the merits and issue a decision resolving the matter in a matter of months. A temporary order in the coming weeks halting the release -- assuming a lower court doesn't do so -- will give a preview of how seriously the Supreme Court is taking the claims.

"I think we'll know pretty promptly what the Supreme Court majority's view is," said Greg Lipper, a constitutional and criminal lawyer in Washington, DC.

"This is a situation where you can't you know you can't unring the bell, obviously," Lipper said, referring to the upcoming deadline. "So, if they are at all sympathetic to Trump's claims they will presumably enjoin the release."

What kind of wiggle room does Trump have to push his legal case?

Trump is making two major claims in the lawsuit: one, that Congress' request for the documents is invalid because it allegedly lacks legislative purpose and two, that, as a former President, he should be allowed to assert executive privilege even as the current President has declined to.

The first legal claim relies significantly on the Mazars case, though the judiciary will be considering those questions under very different circumstance than what was before it during the House's quest for Trump's tax returns. For the latter question, about Trump's ability to assert executive privilege while he's out of office, the legal territory has not been well-trod. Even if Trump is destined to lose, the open nature of issue may entice the Supreme Court to get involved and give a full hearing to the case.

The most relevant Supreme Court case on the executive privilege question is Nixon v. General Services Administration, where the Supreme Court was resolving a dispute brought by former President Richard Nixon over whether the GSA could obtain his presidential records under the newly enacted Presidential Records Act.

The Supreme Court, rejecting Nixon's claim that the law was unconstitutional, said that an incumbent president was in "the best position to assess the present and future needs of the Executive Branch, and to support invocation of the privilege accordingly."

Even legal experts who are largely skeptical of Trump's arguments acknowledge that decision a little bit of wiggle room for courts to consider. The Supreme Court's opinion said that former president "may also be heard to assert" privilege claims.

"There's a recognition [that] there's an interest in the former president, but how significant of an interest is unexplored," Shaub, the former DOJ attorney, said.

It's possible that the courts could decide there are some circumstances where judges should consider former presidents' assertion of privilege, but still rule against Trump in this particular case. Trump is also arguing that Congress' request for his records be thrown out because the investigation of the sort that the House select committee is pursuing is outside the legislative authorities established by the Constitution.

There are plenty of examples of potential legislation coming out of the probe that the House committee could point to in the case, according Eggleston, the former Obama White House Counsel.

The House could also argue that "we have the power to investigate an armed assault against our institution," Eggleston said. "I don't see a court saying, 'Oh no you just have to sit on your hands. ... You have to leave that to another branch of government.' I think that would be a laughable response by a court."