'Congress should come back to D.C. now and FIX THE IMMIGRATION LAWS!,' he tweeted on Monday morning 

Trump made building a border wall and stemming the tide of illegal immigrants a key promise of his 2016 campaign but has shifted the blame to Democrats 

White House is also considering alternative ideas - such as dumping illegal immigrants into sanctuary cities     

President Trump said Monday that he intends to follow through with the plan that the White House insisted was not a serious proposal

'Those Illegal Immigrants who can no longer be legally held ... will be, subject to Homeland Security, given to Sanctuary Cities and States!' he said

Trump said last week that he is giving 'strong considerations' to the issue, following a report that that one of his advisers was shopping the proposal