"That's why we're being so careful with our process and our screening", the president said.
President Trump on Wednesday accused Democrats of wanting a government shutdown so that illegal immigrants could flood into the USA - and bring crime, terrorism and drugs with them.
Democrats want the fix to be included in legislation to keep the government open past Friday. The White House has called for tighter immigration controls and increased border security funding in return.
"The Democrats are really looking at something that is very unsafe for our country", Mr. Trump told reporters at the start of a Cabinet meeting.
"It could happen", Trump said when asked about the chances of a shutdown. "They want to have illegal immigrants, in many cases people that we don't want in our country - they want to have illegal immigrants pouring into our country, bring with them crime, tremendous amounts of drugs", he continued.
Hackers hold NC county's computers ransom for 2 bitcoins
In recent years, companies including Equifax and Target, and also government bodies were attacked by hackers. Hackers are holding county office servers for ransom in the most populous county in North Carolina.
The hard-right House Freedom Caucus is showing an openness to a deal that would prevent a partial government shutdown this weekend.
That puts enormous pressure on House Speaker Paul Ryan, R-Wis., to build a coalition of House Republicans to pass the short-term bill. Republicans have been trying to reach a stop-gap deal to fund the government to at least December 22.
The roughly 30-member caucus has been trying to win promises of tight budget curbs and other concessions from leaders in exchange for backing the short-term bill.
Republican leaders have postponed a planned House vote on the temporary spending measure until Thursday. But on Wednesday he placed blame on Democrats for allowing budget talks to drag this close to the deadline.
The delay shows the clout that conservatives hold.