(CNN) Congress returns Monday from a month-long recess struggling to resolve the difficult politics of gun control while trying to avoid yet another government shutdown in the Trump era.

There are signs that September could be a fruitful month leading to bipartisan deals to keep the government running and continued conversations to change the country's gun laws following a summer marked by gun violence and many calling on Congress to act . But there are also indications that the coming weeks could devolve into a messy, partisan affair that leaves Congress no closer to attempting to stop the spate of mass shootings consuming the country.

A big reason for that question: President Donald Trump has left lawmakers in the dark about what exactly he would accept when it comes to gun legislation.

"I think there's a window of opportunity for the President to lead and to endorse a package of reforms," said Democratic Sen. Chris Coons of Delaware, who has engaged in bipartisan talks over the past month over gun legislation. "I'm torn between hope and skepticism."

Behind the scenes, Senate Democrats and Republicans have engaged in a series of talks with senior White House staff about a package of gun reforms that could form the basis of legislation. But the White House has yet to formally propose a legislative package because Trump has yet to indicate his preference, according to lawmakers and aides in both parties.

Republican sources told CNN that they need Trump to throw his support behind more expansive background checks in order for GOP senators to get behind such legislation. A big reason why: 29 GOP senators who still serve in the Senate voted in 2013 against legislation drafted by Sens. Joe Manchin, a West Virginia Democrat, and Pat Toomey, a Pennsylvania Republican, to expand background checks on commercial sales . And in order for GOP senators to change their position now, they'd need cover from Trump to take the heat from their base and the National Rifle Association.

As part of the Democrats' continued push to keep the pressure on the President to take up gun legislation, Senate Minority Leader Schumer and House Speaker Pelosi sent a letter to Trump Sunday arguing he must intervene to get Congress to act.

"We implore you to seize this moment when your leadership and influence over Republicans in Congress on the issue of guns is so critical," they wrote. "We believe you have a unique opportunity to save American lives by giving political cover to your fellow Republicans to finally pass meaningful gun safety legislation."

Gun talks continue from the summer

Talks between White House staff -- led by senior aide Eric Ueland -- have intensified with aides to Democratic and Republican lawmakers in both the House and the Senate. The President's daughter and senior adviser, Ivanka Trump, along with her husband Jared Kushner, also have spoken to lawmakers, as has White House counsel Pat Cipollone, according to two congressional sources.

Among the topics under consideration: Legislation to incentivize states to enact "red flag" laws to deny access through a court order to firearms to individuals deemed a risk; improve reporting to the National Instant Criminal Background Checks system ; bolster mental health funding and expand background checks on commercial sales, according to several sources involved in the discussions.

But it's far from clear what Trump will ultimately endorse. And if he does get behind background checks, it will almost certainly fall well short of the sweeping universal background checks bill passed by the House, which also would require checks of purchasers in private transactions.

"What is going through White House's mind can literally change from day to day," said Democratic Sen. Richard Blumenthal of Connecticut who told CNN he is "very close" to a deal with Senate Judiciary Chairman Lindsey Graham, a South Carolina Republican, on legislation to provide grants to states to develop red flag laws. "My personal view is that we should do as much as possible, as quickly as possible to save as many lives as possible."

Trump, himself, continues to toy with moving on legislation similar to the Manchin-Toomey proposal. At a closed-door meeting between Trump and Manchin last week at the White House, the President asked Manchin if his bill would lead to the creation of a national gun registry, a fear of the NRA, and Manchin denied that it would, according to a source briefed on the meeting. The meeting was described as productive, though the President made no commitments, according to the same source.

Republican senators are waiting for a signal from the President.

"We do need to have the discussion," said Indiana GOP Sen. Mike Braun, a freshman. "I come from a state where the Second Amendment is very important. It is to me as well. Sometimes conservatives drag their feet on getting engaged in the conversation, and I think this is an example where we need to discuss all the things we can do that are common in sense in nature to keep guns out of the hands of criminals."

Coons added: "I've spoken to a number of my Republican colleagues who say they're not going to take a bold policy position here unless they have the President come out and support something."

How the gun debate connects to funding the government

There are signs that the two issues -- funding the government and gun control -- could quickly get intertwined, as Democrats push for more funding to study gun violence, a topic that Republicans and the NRA has vigorously fought against.

Senate Republicans will be working in committee to pass their 12 appropriations bills when Congress returns with Senate Appropriations Chairman Dick Shelby, an Alabama Republican, first trying to move a "minibus" legislative package -- or a collection spending bills that cover only part of the federal government as opposed to an "omnibus." Shelby's minibus would fund the Departments of Labor, Health and Human Services, Defense, Energy and Water and foreign operations. But, the House-passed version of the HHS appropriations bill includes a provision that spends $50 million to study gun violence in the country, a provision Republicans consider a poison pill.

"The reason our committee was so successful last year is that we made the decision early to not open the bill to controversial issues," Missouri Republican Sen. Roy Blunt, the subcommittee chairman said in a statement. "I'm hopeful we do the same thing this year, which would mean we wouldn't change things that have been traditionally in the bill or attempt to fund partisan priorities."

Given the time constraints, it's not clear that Republicans and Democrats in the House and Senate will be able to quickly pass even one minibus before the deadline. House Democrats passed 10 of the 12 appropriations bills already this year, but the Senate has yet to pass one. The House also has to lower their topline numbers for their bills after the House and Senate struck a budget deal in July that set new caps.

House Majority Leader Steny Hoyer announced last week his chamber will vote on a short-term continuing resolution to fund the government during the week of September 16. The preference of House Democrats, according to one aide involved in discussions, would be to pass all of the appropriations bills at the same time rather than pass a minibus and leave a showdown for later over a few controversial bills like the one for funding for Department of Homeland Security, which would no doubt include fights over the handling of the humanitarian crisis at the border and wall construction.

Already, Republican and Democratic aides concede leaders will likely need a short-term continuing resolution to keep the government funded past September with the fight over appropriations taking center stage in the next month. But, leaders will also have to balance the appetite by some Republican and Democratic rank-and-file to take action on guns even as Senate Majority Leader Mitch McConnell has said he needs to hear exactly what the President will sign before the Senate acts.

"If the President took a position on a bill so that we knew we would actually be making a law and not just having serial votes, I would be happy to put it on the floor," McConnell told Hugh Hewitt last week. "The administration is in the process of studying what they are prepared to support if anything, and I expect to get an answer to that next week. "