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WASHINGTON — President Donald Trump's decision to rescind the federal program protecting undocumented children has handed Congress a task they have not yet proven able to accomplish: address the fate of Dreamers, as participants in the DACA program are known.

While Democrats slammed the president for removing legal protections for as many as 800,000 people as "heartless," "shameful" and "cruel," Republicans mostly said they support the decision to hand it over to Congress.

But what a legislative fix might actually look like is not at all clear and any proposal could become quickly mired in the political cross-currents of immigration legislation that have plagued Congress for two decades.

The political land-mines are especially deep with the GOP itself, where strong grass roots demands for increased border control and opposition to any measure that would grant legal status to immigrants in the U.S. have stymied comprehensive immigration reform in the past.

One thing Republicans could mostly agree on Tuesday, however, was that President Barack Obama's executive order establishing the DACA program was wrong.

House Speaker Paul Ryan called DACA "well-intentioned" but said it was a "clear abuse of executive authority." He said it’s his "hope" that Congress acts.

"It is my hope that the House and Senate, with the president’s leadership, will be able to find consensus on a permanent legislative solution that includes ensuring that those who have done nothing wrong can still contribute as a valued part of this great country," Ryan said in a statement.

Related: Trump Ends DACA Program, No New Applications Accepted

Democrats are already putting the pressure on Republicans to act — and soon.

House Minority Leader Nancy Pelosi called the announcement a "deeply shameful act of political cowardice and a despicable assault on innocent young people in communities across America."

"Speaker Ryan and the Republican House leadership must bring the DREAM Act to the floor for a vote without delay," Pelosi added, referencing a languishing legislative effort to address the issue.

But Senate Majority Leader Mitch McConnell waited nearly three hours to put out a short, vaguely worded statement that didn't even mention DACA, perhaps indicating that he's in no hurry to delve into the pitfalls of immigration policy.

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"President Obama wrongly believed he had the authority to re-write our immigration law. Today’s action by President Trump corrects that fundamental mistake," McConnell said in a statement. "This Congress will continue working on securing our border and ensuring a lawful system of immigration that works."

Despite McConnell's lack of commitment to acting swiftly, other Republicans appeared committed to trying.

Sen. John Cornyn, R-Texas, the second-ranking Republican in the Senate, said "it’s important for us to achieve a long-term resolution."

But what that legislative fix looks like is where it gets complicated. Some have suggested that it could become part of a larger deal to fund Trump's border wall, but Sen. Dick Durbin, D-Ill., immediately panned that idea, calling it a "non-starter."

The White House could release a "menu of options" Congress could pair DACA legislation with as early as this week, said Marc Short, Trump's top legislative affairs aide.

Related: Trump's DACA Move Could End Up Dividing Both Parties

Predicting the legislative battle ahead, Sen. Mike Lee, R-Utah, who has been critical of the way DACA was implemented, said "a balance between compassion and deterring future illegal immigration can be found."

Sen. Ron Johnson, R-Wisc., pointed to a list of things that should be addressed should Congress address Dreamers, indicating that he'd like to see a larger bill as opposed to one focusing just on DACA.

"The president has given us six months to get our act together and fix our broken legal immigration system, end incentives for illegal entry, lawfully protect the Dreamers, and secure or borders," Johnson said in a statement. "I look forward to working in a bipartisan fashion to advance humane, common sense legislation to do just that."

Sen. Tom Cotton, R-Ark., said he'd support DACA legislation in exchange for action on his proposal that Trump previously endorsed that would cut the level of legal immigration in half — a measure that many predict wouldn't even garner 20 votes in the Senate.

My statement on the rescission of DACA: https://t.co/yCjpw0cO5o pic.twitter.com/pSydF8w4gB — Tom Cotton (@SenTomCotton) September 5, 2017

Sen. Lindsey Graham, R-S.C., and Durbin introduced bipartisan long-standing legislation again earlier this year that would directly address the issue. It would provide a path to citizenship for Dreamers through education, long-term employment or joining the military.

"If there was ever a win-win in modern times, it is the DREAM Act," Graham said a news conference Tuesday. Graham supported Trump’s decision to wind down DACA, calling it presidential "overreach."

On Wednesday, Graham shot down Sessions' claim that Dreamers were taking jobs from citizens.

"Jeff Sessions is wrong," Graham told NBC's "TODAY" Wednesday morning, referring to the U.S. attorney general's claims that DACA denied jobs to "hundreds of thousands of Americans."

"These kids are not taking jobs from American citizens, they're part of our country," Graham said.

In a sign of progress, Sen. Cory Gardner, R-Colo., announced that he's signing on as a co-sponsor to the DREAM Act.

They called on the Senate to move quickly and pass legislation as early as September. But Cornyn said that's not going to happen.

"There’s no way," Cornyn said, adding, however, that, "We will take that up. I’m confident."

Sen. Thom Tillis, R-N.C., said in a nine-tweet thread that he will offer his own, more conservative, legislative fix. He says that it would be a “rigorous” path to citizenship that prohibits Dreamers from obtaining public assistance.

The path to earn legal status would require them to be employed, pursue higher education or serve in our military. (7/9) — Senator Thom Tillis (@SenThomTillis) September 5, 2017

And, this is likely to be an issue for the 2018 election cycle. One of those likely to be impacted most could be Sen. Jeff Flake, R-Ariz., who is up in a state that is home to many immigrants but is also highly polarized. Trump pardoned the controversial Arizona sheriff, Joe Arpaio, last month.

Congress must act immediately to pass permanent, stand-alone legislation to lawfully ensure that children who were brought here... 4/5 — Jeff Flake (@JeffFlake) September 5, 2017

Few Republicans criticized Trump but Sen. John McCain, R-Ariz., said it was the "wrong" decision to make.

"While I disagreed with President Obama’s unilateral action on this issue, I believe that rescinding DACA at this time is an unacceptable reversal of the promises and opportunities that have been conferred to these individuals," McCain said.

Congress has voted on the DREAM Act before. In 2010 they voted for a bill that would give eligible undocumented immigrants a path to legalization, but of the three Republicans that voted for it, only one is still in the Senate — Sen. Lisa Murkowski, R-Alaska.