Republican John Kasich, the governor of Ohio, has blasted Donald Trump’s decision to end a policy shielding young undocumented immigrants from deportation, inviting the so-called ‘Dreamers’ to come to Ohio.

Mr Kasich’s comments are part of a stream of bipartisan criticism Mr Trump has received for cancelling the Deferred Action for Childhood Arrivals (DACA) programme, which had been implemented under former President Barack Obama.

In announcing that he was rescinding DACA, Mr Trump called on Congress to let the Dreamers stay in the US. But immigration has been a difficult issue for Congress, and Mr Obama began the programme after a lack of legislative action on immigration reform.

“If the dreamers want to go somewhere and live, come to Ohio,” Mr Kasich said in an interview with CBS. “We want all the immigrants to come to Ohio because we know how much they contribute to America.”

Mr Kasich, whose grandparents were immigrants, added that the President's decision “is not the America that we all love.”

“I wouldn't be in America if it wasn't for immigration,” he said. “Who knows, maybe I’d be the president of Croatia.”

The term Dreamers comes from the proposed DREAM Act, which would have given unauthorised immigrants legal status as long as they met certain requirements. The bill was first introduced in 2001 and has been rejected several times by Congress.

Under DACA, Dreamers were able to apply to defer deportation and legally reside in the US for two years. After that, they could apply for renewal.

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Administration officials have said current programme participants whose permits expire before March 5, 2018, will be able to renew their status if they file applications by October 5. But if Congress fails to act by March, thousands of undocumented immigrants who were brought to the US as children could face deportation.

Mr Trump’s Attorney General Jeff Sessions, along with several other Republicans, have called the Obama administration’s implementation of DACA an “abuse of executive authority”. However, other members of the party have said Mr Trump's decision to end the programme is the wrong approach to immigration policy.

“I strongly believe that children who were illegally brought into this country through no fault of their own should not be forced to return to a country they do not know,” Senator John McCain of Arizona said in a statement. “The 800,000 innocent young people granted deferred action under DACA over the last several years are pursuing degrees, starting careers and contributing to our communities in important ways.”

Now that Mr Trump has punted the issue over to Congress, top Democrats are pushing Republicans to make passing the DREAM Act a priority this fall.

“If a clean DREAM Act does not come to the floor in September, we are prepared to attach it to other items this fall until it passes,” Charles Schumer, the Senate’s top Democrat, announced at a press conference with House Democratic Leader Nancy Pelosi and other colleagues.

“The president’s decision to end DACA was heartless and it was brainless,” Mr Schumer said. “If this order stands, hundreds of thousands of families will be ripped apart, tens of thousands of American businesses will lose hard-working employees.”

But Senator John Cornyn, the Senate’s second-ranking Republican, told reporters “there’s no way” the upper chamber will take up a measure this month that will replace DACA.

He also dismissed the possibility that legislation aimed at protecting young undocumented immigrants from deportation would be in a stand-alone bill, floating the idea that a DACA fix could be tied to border security.

“Border security and enforcement. There may even be some other noncontroversial visa enforcement issues,” he said when asked about what could be included in the legislation.

But while others have suggested that DACA cannot make it through Congress as a clean bill, Republican Senator Marco Rubio said “if you were able to have a stand-alone vote on a good product, [you] could pass it.”

“If you start adding other things to it, that’s where I think it falls apart,” Mr Rubio told Politico.

Republicans’ voicing of different strategies indicates a tough road ahead for any legislative fix for DACA, or immigration reform in general.

The White House has also already signalled that Mr Trump won’t be willing to sign a bill into law that addresses only DACA. “We can’t just have one tweak to the system,” press secretary Sarah Huckabee Sanders said on Tuesday during a briefing.

Meanwhile, Mr Trump tweeted that he would revisit the issue if Congress is unable “to legalize DACA (something the Obama Administration was unable to do).”

He later told reporters he would “like to see something where we have good border security, and we have a great DACA transaction where everybody is happy,” appearing to suggest he wants funds for the construction of a US-Mexico border wall to be included in any immigration reform bill that comes to his desk.

Mary Fan, a law professor at the University of Washington, said comprehensive immigration reform bills that have failed in Congress have tended to pair border fortification measures with policies that could provide legalisation for undocumented immigrants.