There is a movement to make the coming debt limit brawl the last one ever.

As it currently stands, Democrats and Republicans are barreling toward a possible crisis this summer that could be historically ugly and rattling to world markets. On one side, Republicans are demanding that any increase in the government's borrowing authority be paired with steep budget cuts. On the other side, the White House says they won't negotiate on the issue at all.

While it may be too late to head off this year's brinksmanship, a bipartisan group of lawmakers are set to re-introduce an idea in the coming weeks called the Responsible Budgeting Act that, if enacted, would change debt limit fights forever by removing much of the drama around them.

The time has come to "take what's become a political cudgel and turn it into a policy tool," said Rep. Scott Peters (D-CA) who likens the current way debt ceiling debates work to "an exercise in aiming the gun at our own head." He has been a leader pushing the bill alongside Rep. Jodey Arrington (R-TX) in recent years.

"I'm pretty optimistic that we'll have a conversation about it this Congress," Peters added in an interview on Thursday, arguing that the current state of divided government might actually be the best environment to get it enacted.

The debt ceiling was top of mind Thursday amid news that the U.S. government formally hit its borrowing limit, leading the Treasury Department to activate what are known as "extraordinary measures" allowing the government to keep paying its bills for at least a few more months.

“There is a growing appetite for [action to avert future crises], because both parties are increasingly realizing that the debt limit is serving nobody's purposes in its current form,” said Shai Akabas the director of economic policy at the Bipartisan Policy Center in a Yahoo Finance Live interview this week.

“In recent debt limit deals, we've actually seen spending go up, not down,” he added. So, “it is not serving as that focal point for fiscal responsibility.”

Two new ways out of a debt limit crisis

The bill, first introduced years ago, would give Congress two additional off-ramps to tackle the debt limit.

The first option would allow the president to suspend the debt limit if Congress went along by passing a concurrent budget resolution, which includes specific debt-reduction measures.

Failing that, a second avenue to avoid default would allow the president to act alone. But in that case, the debt ceiling could be lifted for a year only as long as the president also filed a written request to Congress, which lays out specific debt-reduction proposals. The full Congress would then be obligated to debate and possibly vote on that proposal from the White House.

Rep. Arrington, in a previous appearance on Yahoo Finance Live, said the proposal leads to "a debate, real proposals, and a vote so that we can actually start taking that trend line and bending it down to a more reasonable and responsible level of debt. That is a much more productive way to do business."

This year, Arrington was selected to serve as the Chairman on the House Budget Committee, giving him a prominent place to participate in Republican debates over the debt limit.

Also fueling hopes that the bill might eventually pass a divided chamber is that it has been led by two lawmakers from opposite sides of the country’s political divide. Peters is a Democrat from the San Diego and Arrington previously worked as a senior advisor to then-President George W. Bush and strongly supported Donald Trump during his time in office.

‘People are very worried about this’

The renewed push to avoid a crisis comes as observers from Washington to Wall Street to Main Street are focusing again on the issue and how dire the consequences of a default could be.

Peters noted during Thursday's conversation that he had just left a forum for the San Marcos Chamber of Commerce in California and that the debt limit was a top issue.

"People are very worried about this," he said.

On what would happen in the event of a default, “we don't know is the honest answer because we've never been there before in modern times,” Akabas said. It would upend the U.S. position as the center of the global financial system and “anything that turns that on its head is going to be extremely concerning to market participants, investors, other global actors,” he added.

Also this week came a glimmer that negotiations could be in the offing when Sen. Joe Manchin (D-WV) said he would support negotiations with Republicans over the debt ceiling that included things like special commissions to look at Social Security, Medicare, and the overall U.S. debt.

Other Democrats for the moment remain steadfast. Senate Finance Committee Chair Ron Wyden (D-OR) released a statement Thursday afternoon saying that Republicans must "stand down on the debt limit immediately.”

For his part, Peters agrees with Wyden and is not pushing to link his bill to any eventual debt limit bill, instead saying Congress should simply lift or suspend the debt ceiling immediately.

But at the same time, he acknowledged, "I understand also that there probably will be conversations about a deal that would get us to lifting or waiving or suspending, and I understand that I will be happy to participate in that, but I don't think that there should be any preconditions myself."

Ben Werschkul is Washington correspondent for Yahoo Finance.

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