If the deal is blocked, the insurance giants would be better off just walking away from a merger agreement that was contentious from the start, analysts said.
"The way that it seems to me is that both Anthem and Cigna are realizing that there is no path to negotiations. There isn't going to be a negotiated settlement," said Ira Gorsky, an event-driven strategist who analyzes mergers at Elevation. "It's in their interest to break as quickly as possible and then get some sort of termination fee."
The two health insurers encountered skepticism from antitrust officials at their most recent meeting with the Department of Justice in late June, according to published reports. That meeting came weeks after contentious emails were made public, showing the two firms have been at loggerheads at times during the approval process.
An Anthem spokeswoman would not comment on the DOJ negotiations. In a statement to CNBC, she maintained that the two companies continue to work toward approval.
"Anthem and Cigna continue to be in ongoing dialogue with the Department of Justice and state regulators regarding the compelling combination of our two companies to increase consumer access to high quality, affordable healthcare," said Anthem spokeswoman Jill Becher.
Leerink analyst Ana Gupte sees the likelihood of the Anthem-Cigna deal being approved as "very slim" at this point. If the deal is blocked, Gupte said she expects it's also unlikely the insurers will fight to overturn a DOJ decision, even at the risk of triggering a hefty break-up fee.
"The merger agreement requires the companies to sue the U.S. government if the deal is blocked," she explained. "Given that [Anthem's] plan B is likely to bid for the Medicare Advantage divestitures available from the Aetna-Humana deal, we do not see it unrealistic that Anthem prepares to walk away from the deal if they can negotiate down the $1.85 billion break-up fee."
A year ago, analysts thought antitrust regulators would scrutinize the Anthem bid for Cigna and Aetna's $34 billion deal to Humana in tandem. Approval of both megamergers would effectively whittle down the nation's five largest health insurers into just a big three — Anthem, Aetna and UnitedHealth.
Now, Elevation's Gorsky said, it appears the DOJ may be more willing to approve Aetna and Humana's deal if Anthem and Cigna remain independent. Together, the Aetna and Humana deal would create a powerhouse in the Medicare market and federal regulators will likely require the pair to make divestitures in certain markets to insure competition.
Since the nation's largest insurer UnitedHealth is already a major player in Medicare, Gorsky expects federal regulators would be more willing to let an independent Anthem or Cigna buy Aetna and Humana's divested assets.
"You now have two other large, strong national players that will have a much bigger position in Medicare Advantage, which should make the Department of Justice more comfortable" about maintaining competition in that market, he explained.
Cigna may be in a better position to pivot to a new acquisition, if the Anthem deal falls through, according to Stifel analyst Thomas Carroll.
"We estimate that Cigna will have swift access to deployable capital of [about] $12 billion that will be put to work as quickly as possible," he wrote in a research note.
But Carroll believes the government also has an interest in approving both deals, and letting Anthem gain greater scale in order to help bring stability to the Obamacare exchange market.
UnitedHealth is pulling out of three state exchange markets in 2017, and a number of insurers are scaling back, because of losses on Affordable Care Act plans.
"The government needs to balance regulatory pressure on the deal with the cost of further withdrawal and potentially losing a strong industry ally," Carroll maintained.
It was clear from the start that the deals would require a protracted regulatory approval process. But since last July, the uncertainty of approval has weighed heavily on Anthem and Cigna shares; both declined about 20 percent over the last 12 months. Over the same period, Aetna's shares lost 4 percent, while Humana lost 6 percent. Shares of UnitedHealth, which sat out the merger dance, rose 16 percent over the last year, to end the second quarter at a new high.