He said he receives questions "constantly" from fellow officials about the "wackier suggestions that are being made" in the race to secure the Republican nomination.
Those proposals include a plan from front-runner Donald Trump that would utilize a federal anti-terror law to require wire transfer companies to check the legal status of immigrants before allowing them to send money home.
Obama, who was speaking from the White House briefing room to deliver remarks about the U.S. economy, called that plan "impractical" with enormous implications. His comments on the state of the 2016 race were in response to reporters' questions.
"The notion that we are going to track every Western Union bit of money that's sent to Mexico -- you know, good luck with that," he said sarcastically, saying that cutting off money to Mexico could damage that country's economy, sending more immigrants to the United States.
Trump's proposal -- outlined in a campaign memo Tuesday
-- would compel Mexico to pay between $5 and $10 billion to construct a border wall by threatening to cut off the remittances. He said he could change a portion of the USA Patriot Act to enact the plan.
"It's an easy decision for Mexico: make a one-time payment of $5 billion and $10 billion to ensure that $24 billion continues to flow into their country year after year," Trump's memo states.
Obama has sharpened his criticism of Trump and other Republicans in recent weeks, calling the tone of the GOP presidential race "vulgar" while suggesting it is harming America's reputation abroad.
On Tuesday, Obama said it wasn't only Trump who was fueling the slide in global standing, singling out some of Texas Sen. Ted Cruz's immigration proposals as "just as draconian."
"People expect the president of the United States and the elected officials in this country to treat these problems seriously," Obama said.
"They don't expect half-baked notions coming out of the White House. We can't afford that," the President said.
Later, White House Press Secretary Josh Earnest -- who on Monday asserted that no damage had yet been done to the United States by Republican candidates -- explained that meetings with leaders had been sidetracked with talk of the campaign.
"Important conversations that are hosted by the president of the United States, or the President's secretary of state, are clouded by these kinds of discussions. It's not good. It's harmful. It makes those meetings less productive than they otherwise would be," Earnest said.
He called Trump and other Republicans' rhetoric counter to U.S. values, which he said "sends a confusing signal" to foreign populations.
"That damage can be mitigated, if not outright eliminated, if the American people choose to elect someone who is serious about advancing American values," Earnest said.