(CNN) Faced with a time crunch ahead of the 2020 election season, the House Judiciary Committee is broadening its investigation beyond special counsel Robert Mueller's findings as lawmakers confront lingering hurdles over impeaching President Donald Trump.

With Congress reconvening next week after its summer recess, the committee is expanding its focus beyond Mueller's findings that Trump may have obstructed justice by seeking to undercut the investigation into his campaign and actions as President, an area that has dominated the panel's focus up until now.

As they head into a critical fall session, Democrats say they will also focus heavily on questions over whether the President is enriching himself while violating the emoluments clause in the Constitution, reports Trump dangled pardons to officials who were at risk of breaking immigration laws and his involvement in hush-money payments to over his alleged extramarital affairs -- all of which could form articles of impeachment against the President, according to lawmakers and aides involved in the effort.

But Democrats privately acknowledge that there are ample hurdles -- the lengthy court battles that are eating into the congressional calendar, uncertainty over whether any new developments could shift public opinion toward impeachment and Speaker Nancy Pelosi's continued skepticism . Yet Democrats hope that the committee shining a spotlight on more of the President's alleged crimes could shift the House's calculus.

"The Judiciary Committee's investigation will be broadening out," Rep. Jamie Raskin, a Maryland Democrat on the Judiciary Committee, told CNN. "It is not all about Russian interference in the 2016 election and the President's efforts to cover up his role in it."

Raskin said the focus needs to be on this: "The central sin, the original sin of the Trump administration, is the decision to convert the presidency into a money-making operation for the President and his business and his family."

In March, the House Judiciary Committee announced a sweeping investigation into a range of potential corrupt activities in the White House, but the focus in recent months has been around what the committee says are five alleged crimes of obstruction of justice detailed in the Mueller probe. Now, Democrats want to shift the focus back to some of the areas that Mueller didn't address -- all of which Trump dismisses as presidential "harassment" and an effort to "redo" the special counsel's probe.

"You know that we focused quite a bit on the Mueller report, even having Robert Mueller before us," said Rep. Madeleine Dean of Pennsylvania, a Judiciary Committee member. "But we always knew his scope was limited ... and so there are other areas of abuse of power."

Democrats divided

There is still dissension over the strategy, with a bevy of lawmakers in districts that Trump carried -- particularly freshmen -- wary about moving forward.

Plus, some Democrats on the House Judiciary Committee are urging the panel not to focus heavily on the hush money, worried a skeptical public would compare that to the GOP push to tarnish President Bill Clinton's reputation amid his affair with a White House intern. And Pelosi privately told her colleagues last month on a conference call that the public still isn't ready for impeachment.

Democrats advocating impeachment say they must drill home this point in the coming weeks: that if Trump weren't President, he would be charged with crimes, and the only reason he hasn't is because of Justice Department policies saying a sitting president can't be indicted. So Democrats say it's up to them to make it clear to voters this fall that the only remedy is impeachment.

And that's the case that some members have been making to voters over the recess, as well.

Rep. David Cicilline of Rhode Island, a member of the House Judiciary Committee who supports impeachment proceedings, said voters have had this constant refrain over the recess: "When are you going to get this guy out of there?"

"I say I'm working on it," Cicilline said.

The House Judiciary Committee has taken several steps in recent weeks that could lead to high-profile hearings, but it's still not clear if those hearings will materialize before the end of the year -- when House Judiciary Chairman Jerry Nadler, a Democrat from New York, says he hopes to decide whether to bring forward articles of impeachment.

House Democrats' subpoenas have been routinely dismissed by the White House, complicating their efforts to get information but potentially giving fodder to their argument that the President is flouting the law.

The committee's lawsuit to compel the testimony of former White House counsel Don McGahn , a key witness in the Mueller report on obstruction, could see a ruling from a federal district judge as soon as November, but appeals could stretch that court battle into 2020. Efforts from other congressional committees to obtain financial information from the IRS and from banks and accounting firms used by Trump and the Trump Organization -- which could become part of an impeachment case -- are also still tied up in court , as is the House Judiciary Committee's effort to get grand jury information from the Mueller probe.

So the committee has begun exploring other potential avenues. Last month, the committee issued three subpoenas — to former Trump campaign manager Corey Lewandowski and former White House aides Rob Porter and Rick Dearborn — seeking to bring them in for public testimony on September 17. The committee also issued a subpoena to the Department of Homeland Security on Wednesday for documents related to reports of Trump allegedly dangling pardons tied to his immigration policies.

And the committee has authorized subpoenas to three individuals tied to the hush-money payments -- including David Pecker, the chairman of National Enquirer parent company American Media Inc. -- although those have not been issued.

"I try not to worry about the clock," Dean said. "I really do count on Congress as a coequal branch to do its job and make sure to get our oversight done as quickly as possible. ... The American people are entitled to the truth before the election."

'People are exhausted by the chaos'

Nadler is party to a lawsuit brought by House and Senate Democrats against the President over the emoluments clause of the Constitution, which says no person holding office can accept gifts from foreign states without the consent of Congress. The issue has been a constant criticism from Democrats since Trump took office, but it's taken on an added sense of urgency this past month as the President has pushed to hold next year's G7 summit at his Trump National Doral Miami golf resort and Vice President Mike Pence stayed at Trump's golf resort in Doonbeg, Ireland — far from his official meetings in Dublin.

On Friday, the House Oversight and Judiciary committees said they were seeking information from the Trump administration surrounding Pence's Ireland stay and Trump's G7 push, sending letters to the White House, Secret Service, vice president's office and Trump Organization.

Cicilline said focusing on those matters -- the President enriching himself potentially in violation of the Constitution -- is a better strategy for the House Judiciary Committee, rather than areas that could be dismissed by the public as salacious, like the hush money, though he did contend that the matter was serious since the President may have broken campaign finance laws. He said many in the public could view the hush-money scandal as old terrain since his alleged extramarital affairs would have occurred before he became President. Trump has denied having affairs with the two women.

"People are exhausted by the chaos," Cicilline said, speaking of the Trump presidency more broadly.

Raskin, who has introduced a resolution of disapproval over the emoluments issue, acknowledged that Democrats still had to convince the public to move forward on impeachment. But he predicted that the committee's work on emoluments and other avenues of presidential misconduct would help build the case.

"The broader story is the President's conversion of the presidency into an instrument of self-enrichment. That's a story that's easily comprehensible, the vast majority of the public understands and is also one the framers of the Constitution anticipated," Raskin said. "They built safeguards. I think we'll be able to tell a story that leads naturally to this constitutional remedy."

This story has been updated with additional developments Friday.