The Senate is waiting with bated breath as the Senate parliamentarian considers whether Democrats are allowed to include immigration reform in their $3.5 trillion reconciliation bill, a move that would allow Democrats to circumvent the filibuster and the opposing party on the decades-old issue. 

Democrats made their case this week to Senate Parliamentarian Elizabeth MacDonough that their immigration proposal should survive the "Byrd Bath" – a process of weeding out non-budget related items from budget reconciliation bills named after the late Sen. Robert Byrd of West Virginia. 

"Literally we are in the Byrd Bath," Sen. Dick Durbin, D-Ill., said Tuesday. "A presentation is being made on behalf of the provisions we authored for changing immigration in the United States. That matter is now being considered by the Senate parliamentarian… It is entirely in her hands at this point."

"We believe immigration is a critical element in reconciliation for three reasons," Durbin said, laying out Democrats' case for its inclusion in the bill. "First reason: How many years have we all complained that the immigration system in America is broken and needs to be fixed?"

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As for the other reasons, Durbin argued that the bill will bring $10 back into the U.S. economy for every dollar spent on immigrants newly eligible for new federal programs, and that the economy needs more workers, so giving illegal aliens legal status "gives them a chance to be a functioning part of this economy." 

The budget reconciliation process is unique in that it allows bills to pass through the Senate with only 50 votes, rather than 60, twice every two years. This enables the majority – currently Democrats – to pass bills related to spending and taxation on a party-line basis when they would normally have to secure votes from the other party. 

But those bills go through a process called the "Byrd Bath" that ensures they are indeed related to taxing and spending. That's why Democrats cannot pass voting legislation via reconciliation, for example. Immigration, meanwhile, is more of a borderline issue. 

If Democrats do manage to include immigration reform in the reconciliation bill, it would mark a major development in an issue Congress has tried but often failed to tackle for decades. Efforts under president after president, and in Congress after Congress, have floundered and failed to make major changes to the U.S. immigration system. 

Senate Minority Leader Mitch McConnell, R-Ky. – whose party argued against including immigration reform in Democrats' behemoth spending bill – said he understands why they're trying to shoehorn it into the bill. 

"The way the process works is, the majority which is trying to move a bill … tries to insert something that sounds questionable and there's basically an oral argument before the parliamentarian," McConnell said of the process Tuesday. "Can't blame the other side for trying to use reconciliation as expansively as they want to. That's always the temptation of the majority."

But McConnell warned that Democrats had better not try to disregard the parliamentarian's ruling. 

"Abiding by the parliamentarian is essential to the function of the Senate," McConnell said. 

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But, minutes later, Schumer wouldn't commit to doing so. Asked whether he would consider removing the parliamentarian if Democrats get an adverse ruling on immigration reform, Schumer did not deny that he would. 

The majority leader instead said he's had positive conversations with MacDonough and that he expects such conversations to continue. 

Democrats are currently negotiating amongst themselves in an effort to come to an agreement that can pass the House and Senate with minimal defections – they can't lose any votes in the Senate and can only lose three votes in the House. 

Progressives are adamant that $3.5 trillion is their floor for the bill's price tag. Moderates are arguing for a total of closer to $1.5 trillion. It's unclear how that gulf will be resolved, and work on the bill is likely to drag into October and potentially beyond. 

Fox News' Jason Donner contributed to this report.