(CNN) Senate Majority Leader Mitch McConnell vowed to move a massive $1 trillion economic stimulus bill at "warp speed. " But on Capitol Hill, warp speed isn't that simple -- and could mean weeks before relief comes.

There are many legislative hurdles and ample policy differences that lawmakers still have to iron out. That's left Republican and Democratic leaders uncertain how quickly a bill can pass Congress, meaning getting a final measure to President Donald Trump's desk next week is currently the most optimistic assessment.

That means industries and workers now under siege from the damaging economic crisis will be forced to wait for the legislative sausage-making to work its course. And once the bill is eventually passed, it will take time to get implemented, including proposed payments to workers who have been displaced because of the unprecedented impact of the novel coronavirus.

While Treasury Secretary Steven Mnuchin asked congressional leaders for a bill to be completed by Monday, Speaker Nancy Pelosi told Democratic lawmakers that is an unrealistic timeframe, according to a source familiar with her remarks. Pelosi pointed to the last round of talks with the Trump administration that continued to drag on over the emergency relief package that was just signed into law, the source said.

Republicans in the Senate seem to share a similar assessment.

"A lot of it depends on how quickly things can come together through the weekend," said Sen. John Thune, the Senate majority whip and a South Dakota Republican. "But then we are going to start the negotiations with the Democrats. And we got a number of our members who will be involved in that and hopefully through the weekend we can bring some closure to it through the weekend and early next week."

Even that is an optimistic scenario, according to Democrats and Republicans.

On a conference call Thursday by the House Democratic Caucus, several committee chairmen detailed their own proposals for the stimulus, with many expressing grave concerns about the growing demands on unemployment insurance benefits and the need for Congress to do more provide assistance to states, local governments, seniors and displaced workers, according to multiple sources on the call.

Pelosi indicated she wasn't thrilled with some of the proposals by Senate Republicans, including trying to move a $45.8 billion emergency funding measure as a separate package; she wants to combine that spending package with the stimulus plan. Democrats are now putting together their own proposal in the House, meaning Democratic leaders and McConnell will have to reconcile several competing proposals and get White House support -- all within days if they want to provide immediate relief.

Once there's a deal, several steps in the legislative process need to play out before the bill can be become law.

First, Senate Republicans are negotiating among themselves and the Trump administration to try to come to Republican proposal on the parameters of the stimulus plan. Then, they will try to reach an agreement with Senate Democrats, who have their own proposal spearheaded by Senate Minority Leader Chuck Schumer.

Schumer, himself, will be consulting with Pelosi -- and both Democratic leaders have been in regular communication with Mnuchin. But the negotiations are only just beginning in earnest. Pelosi and other Democrats have called for immediate negotiations with the four top leaders of Congress and the White House, and some Democrats warned that McConnell's process of trying to reach a GOP deal first would only slow deliberations down.

"This is a crisis everybody says we need to act urgently," said Washington Sen. Patty Murray, the No. 3 Democrat. "If they put together a partisan package and it can't pass the House, or gets tied up over here, that helps no one."

Once a deal is reached over the elements of the bill, the two sides have to draft the bill language -- a time-intensive process, particularly on a bill of this magnitude. That was apparent during the Pelosi-Mncuhin negotiations over the just-enacted coronavirus relief package -- which includes free testing for the disease, unemployment benefits and paid leave to some workers -- and took days to sort out the language even after the two announced an agreement. That measure is smaller in scope than the forthcoming economic stimulus measure.

When the stimulus bill is ready to move forward, assuming the Senate decides to move first, McConnell would have to get consent from all 100 senators to immediately schedule a vote. But there are bound to be objections, with senators eager to change aspects of the bill and demand votes on amendments. Those negotiations take time to sort out. And if McConnell is forced, he could take procedural steps to overrule those objections -- a process that could take several days.

And after the Senate passes its bill, the House would have to take up the same plan, or it may act on its own measure. While the House can move quicker than the Senate, House leaders have told their members they do not need to return until a deal is reached on the stimulus, and would need 24 hours notice to return.

Plus there are many questions among members about how the votes can go forward with a growing number forced to quarantine after two House lawmakers tested positive for the disease. So far, congressional leaders have resisted allowing members to vote remotely.

Still, while there are many obstacles remaining, both sides sense urgency in acting -- and are optimistic a law will be made soon. They just don't know when.

As he left the floor Thursday detailing the upcoming Senate GOP stimulus plan, and as he once again told senators the Senate won't leave town until it's done with the bill, McConnell was asked how quickly he expect the bill to pass. He declined to comment.

This story has been updated with additional developments Thursday.