This is categorically not true. It started with the Immigration Reform and Control Act of 1986. It was pushed in the House by Dem Rep Romano Mazzoli and in the Senate by Rep Senator Alan Simpson. It was signed into law by President Ronald Reagan. It was the first and so far only illegal immigrant amnesty in the nation's history. It opened the floodgates on our southern border and they have not been closed since.
It was Bush I who failed to implement any of the enforcement measures of the 1986 amnesty that insured we would have 30 million illegal aliens as we do today.
There have been at least 5 more amnesty extensions tacked onto that one, not including the Kenyanesian Usurper’s illegal DACA.