Exchanges are online health insurance marketplaces pioneered in Utah and Massachusetts, although the two states have taken very different approaches.
"The Utah model is innovative in its simplicity," he said.
Gov. Herbert asks the president to declare Utah's plan a model for other states. He says the plan required in the federal health care law would include fewer choices and make people more dependent on public programs.
"I am confident that if you make this change, several other states will join Utah and request certification for 'state-based exchanges' based on our model, thus spreading a proven approach that lowers costs and increases access," Herbert said.
Herbert says he needs answers to make a decision by Friday.
There was no immediate response from the White House.
Under Obama's health care law, every state will have an exchange starting Jan. 1, 2014. The exchanges will provide one-stop shopping for individual consumers and small businesses.
Low-income people can find out if they will qualify for coverage through Medicaid. Middle-income people can pick a private insurance plan offered through the exchanges, and in most cases, get federal government assistance to pay their premiums.
Under the law, virtually every American must have health insurance starting in 2014. At the same time, insurers will be forbidden from turning down people in poor health or charging consumers more because of a pre-existing condition. The law also limits what insurers can charge older customers, who are more prone to health problems.
States have three options as far as exchanges: They can build their own; they can run one in partnership with the federal government; or they can default to Washington and let the feds set up and operate their exchange.
So far, 16 states and Washington, D.C., have said they will set up their own exchanges, while 19 Republican-led states have opted to allow the federal government in. Another seven states have picked the partnership model, and the rest are trying to decide. States that want to run their own exchanges have until Friday to submit plans, but the deadline for partnership applications isn't until February.
Opponents of Obama's health care law say there's too much federal micromanagement. But pragmatists say states are better off running their own exchanges because insurance regulation has traditionally been their bailiwick, and because it will allow them to run their Medicaid programs more efficiently.
A recent AP poll found that Americans prefer that states have a strong hand in running the exchanges. Sixty-three percent said states should run the new markets, while 32% preferred federal control. Republicans heavily favored state control.
This is the second letter sent by Herbert to federal officials regarding his state's health insurance exchange. In November, Herbert wrote to Health and Human Services Secretary Kathleen Sebelius asking for help with "far too many unanswered questions" about the federal alternative.
Herbert slammed the U.S. Supreme Court ruling upholding the Affordable Care Act in June, saying that while it "may be constitutional" it's still bad policy.
There are about 400,000 uninsured people in Utah, or about 14 percent of the population, according to figures from the Kaiser Family Foundation.