In an effort to put faces in front of the funding battle, DHS personnel were placed behind Secretary Jeh Johnson at a press conference as he listed his department's duties.

"Counter-terrorism, border security, aviation security, maritime security, cyber security, protection of critical infrastructure in this country—none of this is free," Johnson said.

The Republican-controlled Senate is ready to pass the funding bill, but Senate Democrats are blocking it.

They don't like a provision in the bill, tacked on by House Republicans, that unravels Obama's unilateral executive action on immigration – the move that defers the deportation of some 5 million immigrants living inside the U.S. illegally.

The debate is not over whether the DHS should be funded. Rather, it's about whether Congress should use its power of the nation's purse to stop the president from doing something many Americans think is unconstitutional.

"The executive action the president took late last year was clearly an unconstitutional end run around the law creating authority of the Congress of the United States," Gov. Mike Pence, R-IN, told "Fox News Sunday."

Pence is one of the state leaders from across the country in Washington for the annual governor's conference at the White House.

Obama appealed to governors to put pressure on their representatives in Congress to pass the bill.

"They all work in your states," the president said, "these are folks who, if they don't have a paycheck, are not going to be able to spend that money in your states. It will have a direct impact on your economy, and it will have a direct impact on America's national security."

But the Obama administration is also trying to protect the president's immigration action on another front—after a federal judge in Texas last week put a temporary hold on the move in a case where 26 states are trying to stop the president's plan to protect illegal immigrants from going into effect.

The administration has filed an appeal because the White House would like the immigration order to go into effect while the case is still in the courts.

Meanwhile, some wonder if the White House is really making a strong enough case that it's truly urgent to pass the bill to fund the Homeland Security Department.

In his daily briefing Monday, White House press secretary Josh Earnest had a hard time explaining exactly how national security will be harmed if a funding bill isn't passed.

If an agreement isn't reached, most DHS employees will still be required to report to work, but they won't receive a paycheck until congress appropriates the money. Thirty-thousand employees would be asked to stay home.

And then there's the politics of the situation. Some conservatives argue the president's move to protect illegal immigrants is unpopular with the public. (Screenshot: Illegal immigrants/via CBN News)

Despite that, Republicans worry they will take the fall—even though Democrats are actually the ones blocking the bill from coming to a vote.

"If we don't fund the Department of Homeland Security, we'll get blamed as a party," Sen. Lindsey Graham, R-SC, said.

Some Republicans outside of Washington say the fight to stop the president is worth it. They say he abused his power and violated the Constitution. Even after saying more than 20 times that he couldn't unilaterally move to help illegal immigrants, he did so anyway.

"We need to protect the homeland; we also need to protect the Constitution," Gov. Pence said.

Syndicated columnist Charles Krauthammer is suggesting the GOP should "abolish the filibuster, take control of the Senate, pass the House bill, and send it on to the president."

That, Krauthammer reasoned, would give the president a tough choice that would "change the narrative."

"If you send it on to the president and he has to do a veto, a public act where he vetoes the funding for the department, the narrative will be that the president—in order to protect an unlawful action on immigration that is extremely unpopular anyway—is risking the security of the country," he told Fox News "On the Record" anchor Greta Van Susteren.

"That's a better narrative, and I think it puts pressure on the president to come to a compromise or to cave on this, which I think is what the Republicans should want," Krauthammer concluded.

Funding for DHS runs out at midnight on Friday.

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