Herbert is part of the National Governors Association executive committee, which sent the six state leaders to meet with Obama and Vice President Joe Biden.
NGA President Jack Markell, the Democratic governor of Delaware, said the group didn't take a political stand supporting one proposal over another, but instead offered its assistance to come up with ideas as Congress and the president try to reach an agreement by the Dec. 31 deadline that would help the economy, while also reducing the national debt.
Obama asked Biden to continue working with governors as they come up with ideas to shave federal spending or make programs more efficient.
Herbert has been highly critical of the Obama administration for not including governors in major policy debates, such as health reform.
"We've been kind of ignored in the past," he said. "Asking us for our opinion and our thoughts is a positive thing."
After his meetings on Capitol Hill, Herbert said he felt "cautiously optimistic" that Congress and the president will reach a compromise eventually, though the game of "high stakes poker" may last a while longer.
"Although they are far apart, I'm hopeful they will find a solution," Herbert said. "Heaven knows that Americans need a solution."
Obama is demanding that Congress let the tax cuts passed under President George W. Bush expire on incomes above $250,000, something congressional Republicans have rejected out of hand.
Herbert has resisted tax rate increases, but like many Republicans in Washington, has said the government could collect more tax revenue by limiting deductions and tax loopholes for the wealthy.
But for him the issue is far broader than the contentious tax debate. He is worried that inaction could zap as much as $500 million in revenue from Utah, largely because of an expected economic downturn, at a time when the state's job market is improving.
Herbert and Oklahoma Gov. Mary Fallin, also a Republican, told reporters they urged the president to give the states flexibility when it comes to implementing federal programs and tackling expected budget cuts.
"We also are saying that states are willing to do our part. We understand that there is going to be a share of sacrifices, as you have to look at spending cuts," Herbert said. "States are willing to do more with less. We're asking for more flexibility."
What states will resist is any move to delay action on the impending spending cuts or tax increases, arguing that businesses need certainty to invest and grow the sluggish economy.
"They can't postpone any of it." Herbert said. "The governors would like to see them do it all now. Get it done."
Other governors who participated in Tuesday's meetings included Arkansas Gov. Mike Beebe and Minnesota Gov. Mark Dayton, who are Democrats, and Wisconsin Gov. Scott Walker, a Republican.