Republicans, who are seeking spending cuts, urged President Barack Obama to apply what's known as the "sequester" in a more careful way, rather than slashing budgets across the board.
The White House has issued dire warnings about the impact the cuts will have, including mass temporary layoffs or "furloughs" in the military, a slowdown in air traffic, and shutdowns for daycare programs and meat-processing plants.
"They've rolled out this great political theater about how cutting less than 3 percent of the federal budget is going to cause all these awful consequences," said Louisiana Governor Bobby Jindal, a Republican, on NBC's "Meet the Press."
"Here's his chance to say, 'Here's how we can do it better,'" Jindal said, suggesting Congress and the White House give departments the ability to cut spending on less essential services.
Congress returns on Monday after a week-long recess and unless lawmakers reach a deal with the White House to postpone the sequester cuts, they will take effect on March 1.
Obama has urged Congress to buy more time for a broad budget deal with a short-term measure that boosts revenues by ending some tax breaks for the wealthy.
Senate Democrats have put forward a plan that focuses on those tax loopholes. This week, Republicans are expected to propose alternatives.
"I think this notion of giving the President the discretion to make the spending cuts - I think that's a cop-out. So I will be urging my colleagues to have an alternative and for us to present one," said Senator Kelly Ayotte, a Republican from New Hampshire, on CBS's "Face the Nation."
WASHINGTON, SOUTH TO BE HARDEST HIT
Governors, in Washington this week for an annual meeting, are concerned about the impact of the cuts on jobs and the economy at the state level.
On average, government programs subject to the cuts provide 6.6 percent of states' revenues, according to Pew Center on the States.
Obama is slated to speak to the group at 7:10 p.m. EST (0010 GMT Monday) at a White House dinner on Sunday night.
An analysis by Wells Fargo Securities Economics Group last week found that under sequestration, states close to the nation's capital and in the South will be hardest hit.
White House officials have said the sequester law does not allow the administration to be flexible in applying the cuts.
"We don't have any ability with dumb cuts like this to figure out what the right thing to do is," Education Secretary Arne Duncan said on "Face the Nation."
"There are literally teachers now who are given pink slips, who are given notices that they can't come back this fall," Duncan said.
In recent weeks, the White House has staged a series of events to illustrate how the cuts will affect American jobs, and has focused on pinning the blame for the looming cuts on Congressional Republicans.
Republicans have fought back by saying the sequester mechanism - part of a 2011 law designed to force Congress to reach a deficit reduction deal - was Obama's idea.
On Sunday, the Washington Post's Bob Woodward waded into that fight, saying White House officials including Jack Lew - Obama's nominee for Treasury Secretary - proposed the sequester.
In an opinion piece, Woodward said Obama was "moving the goal posts" by insisting on new tax revenue as part of an alternative to the sequester cuts.
"His call for a balanced approach is reasonable, and he makes a strong case that those in the top income brackets could and should pay more. But that was not the deal he made" in 2011, said Woodward, who wrote a book about the deal called "The Price of Politics."
But an administration official said Obama had always said that he would push to replace the sequester cuts with a mix of spending cuts and tax revenue.
"The sequester was understood by all parties to be an enforcement mechanism that would be mutually odious enough to bring both parties back to the table to negotiate a 'Grand Bargain' with both entitlement savings and revenues to replace it," said the official, on condition of anonymity.
LOTS OF TALK, LITTLE NEGOTIATION
Rhetoric aside, there has been almost no negotiation between the White House and Congress on the March 1 cuts, although Obama phoned Republican leaders last week to discuss the issue.
"The president should be calling us over somewhere, Camp David, the White House, somewhere, and sitting down and trying to avert these cuts," said Republican Senator John McCain on CNN's "State of the Union."
Democratic Congressman Eliot Engel agreed that Congress should seek "smart" cuts, rather than across-the-board reductions.
"I think Congress should sit down and avoid the sequester," Engel said on ABC's "This Week."
"And if the sequester kicks in, for a week or so, we should then fix it so it doesn't become a permanent thing," Engel said.
(Additional reporting by Aruna Viswanatha, Tabassum Zakaria, Lisa Lambert and David Brunnstrom; Editing by David Brunnstrom and Eric Walsh)