Washington (CNN) A federal judge in Washington cast doubt on Tuesday that the courts could limit Congress' ability to investigate President Donald Trump, in the first major hearing over congressional subpoenas for Trump's financial records.

The court case is testing whether a Democratic-led House committee can obtain financial records from Trump's accounting firm.

On Tuesday, the subpoena arguments became a classic separation-of-powers fight -- with questions of whether the President broke the law in his business dealings hanging over it.

Judge Amit Mehta of the US District Court for the District of Columbia began the session by highlighting just how unusual it would be for the federal court to narrow a congressional inquiry and how problematic for him to rule in a way that predicted future legislation.

"Am I right there isn't a single Supreme Court case or appellate case since 1880 that has found a congressional subpoena overstepped its bounds?" Mehta asked Trump's lawyer. "I agree there are outer limits, but it's not clear to me what they are."

Mehta said he would not rule on the subpoena this week.

Mehta also noted how Congress has done historically important work with investigations in the past, like in the Watergate and Whitewater investigations.

"Shouldn't I be presuming in this case that what Congress is doing is constitutional?" Mehta said as he questioned Trump's side. Considering what Congress could do with what information it gathers "frankly strikes me as opinion-driven judicial decision making," he said.

During the 90-minute arguments, Trump's legal team revealed just how much they want the courts to curtail Congress, while Congress believes its investigative actions could lead to legislation, keeping their activities within the Constitution.

William Consovoy, an attorney representing Trump, told the judge that Congress shouldn't get close to criminal probes.

"This is an effort to engage in law enforcement, not to legislate," Consovoy said.

Yet Doug Letter, the House general counsel, told the judge that informing its members and the public is a key piece of what Congress does.

"Congress is not trying to send President Trump to jail," he said. "But we can still look into ... whether someone is violating the law."

In this case, the Democratic-controlled House Oversight Committee has subpoenaed the accounting firm Mazars USA for all financial statements, communications and other documents related to Trump, a handful of his companies and his foundation from 2011 through 2018.

Trump's personal legal team then sued Mazars to stop the subpoena, prompting the House to step up in court to argue for its investigative request.

The case weighs the extent of Congress' authority and the personal privacy claims of the President in a court system that's generally refrained from infringing on congressional investigations, including subpoenas.

All about timing

In this case, timing may be everything.

So far, the President's legal team has said Mehta is moving too quickly. Even if the Trump team were to ultimately lose the case, the federal courts could be used to tie up the subpoena for months -- potentially past the 2020 elections.

The judge responded on Tuesday that he would move the case along and wouldn't let the Trump legal team drag out attempts to seek documents or offer more arguments. Instead, Mehta will have all information he needs by the end of this week, and will issue his ruling in writing.

"No judge would make a hasty decision on such important issues," Mehta said in court.

In addition to Mazars, Trump is trying to stop two banks from fulfilling separate House subpoenas for his records.

The accounting firm and banks haven't taken sides in the cases. Instead, the House general counsel is arguing opposite Trump.

Michael Cohen's allegations

Mazars became a target in the House investigation after former Trump personal attorney Michael Cohen accused Trump of fudging his wealth in an unsuccessful attempt to buy the Buffalo Bills football team and reduce his real estate tax burden.

The House has argued that it has the authority to subpoena Trump's information, and says it is investigating potential constitutional, conflict of interest and ethical questions related to Trump's financial holdings.

Letter, the House attorney, compared this investigation to several other moments in history. Jumping on Mehta's earlier historical allusions, Letter repeated that congressional investigations into the September 11 terrorist attacks, the Iraq War, Whitewater and Watergate served "an extremely informative function for the American people."

Letter also raised some hypothetical possibilities of how Congress' subpoenas could lead to legislative reform -- such as how turning up information could almost always affect congressional appropriations.

"Mr. Consovoy seems to be saying Congress can't regulate the President. I say, 'Oh yeah?' " Letter said. He conceded that only some extremely personal probes of the President -- like a request for a childhood diary -- wouldn't be within Congress' parameters.

Trump's attorneys, conversely, say the President is being targeted by the Democrats for political reasons and that the subpoena doesn't have a legislative purpose. They also argue Trump will be harmed if his private information from his accountant is exposed.

Those arguments didn't work in at least one recent court challenge of a congressional subpoena -- when the opposition research firm Fusion GPS tried to block a bank from turning over its financial records to House Republicans.

The House Financial Services and Intelligence committees are also investigating the President's finances and have delivered subpoenas to Deutsche Bank, Capitol One and other major banks.

Trump, his businesses, and three of his children -- Ivanka, Donald Jr. and Eric -- are suing in New York federal court to stop the subpoenas to those banks and won't be heard by a judge until next week.

During the hearing Tuesday, the House of Representatives' lawyer admitted that a memorandum of understanding exists between at least two committees -- apparently Oversight and the Financial Services committees, according to the court hearing -- regarding document requests that relate to Trump and a bank. That coordination has "nothing to do with" the inquiry into Mazars, Letter said.

Trump's team said it will try to get that document to show the court how the House is politically coordinating.

Separately, a fourth Democratic-controlled House committee, Ways and Means, issued a subpoena late last week for Trump's tax returns from the IRS.