Ecclestone confirmed over the weekend in India he had proposed to the 12 teams the possibility of a cap of 250million US dollars (£155m) which would include all costs, including driver salaries.
The notion of reducing exorbitant costs in F1 has long been mooted, notably since the end of 2009 after three major manufacturers in BMW, Toyota and Honda had pulled out of the sport in the space of a year.
The resource restriction agreement (RRA) has since been on the table, but has faced strong opposition from Red Bull, in particular, and Toro Rosso.
Frustrated at the lack of progress, Ecclestone has now proposed the kind of budget cap figure under which every team could comfortably operate.
It is understood, for instance, Red Bull's total spend last year en route to winning both championships was 270m US dollars (£168m).
But Whitmarsh believes it is flawed as he said: "It (the 250m US) sounds like quite a lot of money, so I don't know how much it is going to help many teams.
"The philosophy on controlling costs in Formula One is important to our sport and we all agree on that, although there are different opinions as to how that is best achieved.
"Bernie wants one that controls driver salaries and all those kind of things.
"What we should be trying to do is ensuring we are spending money in the appropriate places and controlling excessive spend in development.
"Personally, I think it's a little unrealistic to have a global budget cap because it becomes even more difficult to pin down and to know everyone is comfortably operating within it."
For Whitmarsh, the RRA pioneered by McLaren, he feels is a more workable solution.
"The budget cap from Bernie has the elegance that you can describe it quickly, but it is very difficult to find out where the money is and control it," said Whitmarsh.
"The resource restriction agreement asks: How much money do you spend externally and how many people do you have? It's difficult to hide either of those.
"They're also the core elements of a budget cap, but then it goes on to wind tunnel hours, CFD (computational fluid dynamics) etcetera, and we should be free to pay drivers whatever we want to pay them.
"What we should be doing is finding the easy, clear, measurable, definable elements of spend and control those.
"They (the RRA and budget cap) are both trying to do the same thing. They're not against each other. They're just a different philosophy."
Lotus team principal Eric Boullier, however, can see the benefits of Ecclestone's idea, but believes further discussion is required.
"Bernie is very serious," said Boullier.
"The budget cap is one of the best ways to have control over useless expenditure and to end the competitive war.
"Clearly, this is a good start, that Formula One starts to understand and to put in place a budget cap, and I can back up Bernie's idea.
"You need to do it in a clever way and build it up over the years, and it's something that could happen because it's coming from the right authority."
Asked whether it was a better idea than the RRA, Boullier added: "I don't know yet.
"We have been working for years on the RRA, and we have a better understanding of what we could achieve with that. It's a complex system.
"The idea of a budget cap from Bernie is quite new and we just need to look at it a bit more."