Some EFL clubs will "disappear within five to six weeks" unless they get financial support, says Nigel Travis, chairman of League Two Leyton Orient.
He also said 'Project Big Picture' - a plan by Liverpool and Manchester United to reform the English football pyramid - was a "great proposal".
The idea includes reducing the Premier League to 18 clubs and scrapping the EFL Cup.
In return, the EFL would get 25% of all future TV deals plus a £250m bail-out.
"If clubs don't get something soon you will see clubs disappear, I would predict, within 5-6 weeks," Travis told BBC Radio 5 Live.
But he added: "One thing I need to quash is, this isn't about the pandemic, this is about a crisis in football that goes back many years.
"Before the pandemic, 75% of clubs were losing money - that can't continue. The pandemic has, if you like, exacerbated the problem and we need to get it fixed.
"I know you are talking about 'Project Big Picture' - this is a great proposal as far as we are concerned. It is certainly very promising and clubs need it.
"Something like this has to go through."
The government has agreed a funding package with clubs in the National League, which allowed their season to begin last week behind closed doors, but there has been no support for EFL clubs, with Culture Secretary Oliver Dowden suggesting the Premier League could support lower-league sides.
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The 'Project Big Picture' proposals
- The Premier League cut from 20 to 18 clubs, with the Championship, League One and League Two each retaining 24 teams.
- The bottom two teams in the Premier League relegated automatically with the 16th-placed team joining the Championship play-offs.
- The League Cup and Community Shield abolished.
- Parachute payments scrapped.
- A £250m rescue fund made immediately available to the EFL & 25% of all future TV deals
- £100m paid to the FA to make up for lost revenue.
- Nine clubs given 'special voting rights' on certain issues, based on their long time in the Premier League.
On Monday, a West Ham source told BBC Sport that the Premier League club are "very much against" the proposal.
"The big six are using Covid for a power grab," said the West Ham source. "If this goes through, over time they will just use more and more for themselves."
However, English Football League chairman Rick Parry is backing the controversial proposals and is adamant those behind the plan will not be deterred, despite fierce opposition from the Premier League, government and fans' groups.
Parry also says the Premier League could have come up with its own plan but has failed to do so.
"The real villains here are the government," added Orient chairman Travis. "They've thrown football into a difficult situation. They said the Premier League has to bail out the EFL.
"I understand that but now they are complaining about what is coming out of some creative people.
"Just to be brutally honest, I live in Boston [in the United States]. I know [Liverpool owner] John W Henry.
"He and I have not personally discussed this but I am supportive of the proposal because this is going to save clubs like Leyton Orient and many other clubs in League One and Two.
"The reality is you need to save football and this is the only and best proposal I've seen. The government did a great job with the furlough programme but they've given the EFL no chance other than to negotiate with the Premier League.
"As of a week ago, as far as I know, all the Premier League came up with was £50m - that is not enough.
"The £250m that has been talked about and the 25% share is clearly going to create a sustainable model and that's what we need in football.
"If there are better proposals, I would love to hear them."
Premier League TV deal link is long overdue - Ridsdale
Championship side Derby County's chief executive Stephen Pearce and chairman of League Two club Forest Green Rovers, Dale Vince, have voiced their support for the plan.
Preston owner's representative Peter Ridsdale told BBC Radio Lancashire that his club "broadly welcomes" the proposals while "recognising that there are some elements that still need further talk and debate".
"For two to three years now, we've been advocating a distribution model that recognised that too much of the cash in the game was going to the Premier League and not enough into the Football League," he said.
"Therefore the elements that I've seen that appear to address that, we're in favour of.
"A suggestion that we link ourselves to the Premier League TV media deal is long overdue.
"We can't have a situation where Championship clubs get £7.3m from the Football League and the Premier League and clubs who have been promoted and then relegated benefit from about £170m for one season in the Premier League. That can't be right.
"It means it's difficult for us to compete, we're competing against clubs with parachute payments and it encourages people to overspend, which can't be good for the game."
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