Speaking on BBC Politics Live, the radio host and former Number 10 advisor claimed it was time the Prime Minister considered to give up on her leadership and make space for someone else to sort out the Brexit mess she created. Mr Swarbrick argued Theresa May has lost control and authority over her own Party and even her own Cabinet and should recognise she is not the person to "bring this together".
Now Mrs May is holding urgent discussions with the DUP ahead of an attempt to bring back her deal for a third meaningful vote.
The Unionists rejected Mrs May’s Brexit deal this week over continued legal wrangling about the Irish backstop.
Across the channel, EU leaders are meeting ahead of a two-day summit next week to decide whether Britain is allowed to get an Article 50 extension or not.
Britain is still scheduled to leave the EU in two weeks on March 29 following two years of negotiations.
But with no agreement about a plan, the UK could go to a “no deal” Brexit if MPs reject a third meaningful vote next week.
On Wednesday, MPs overwhelmingly voted to reject a no-deal Brexit under any circumstances by 321 to 278 votes - but the result was not legally binding.
EU leaders have indicated they would accept a “technical extension” of a few weeks if Mrs May can somehow convince her colleagues to pass her deal.
If this does not happen, the prospect of a no-deal Brexit looms large.
He said: “It’s complete shambles, I’m afraid. There is no way around the fact that this is totally broken down, not just Cabinet’s collective responsibility - which frankly went a while ago - not just the Party’s ability to have authority among its own MPs with whipping arrangements, the Prime Minister’s own authority among Cabinet’s ministers and within her Party.
“The whole thing feels completely broken which is partly why - with absolutely no joy whatsoever - I think it’s time that this Prime Minister looks at her the in office.
“Because I’m not sure she is the person to bring this back together again - if it can be brought back together again once we find ourselves through the current mess we have.”
Last-minute talks are underway in Britain and Brussels to find a solution for Brexit following a momentous week in Parliament.
MPs voted in overwhelming numbers to delay Brexit and extend Article 50, two days after Prime Minister Theresa May’s deal was heavily defeated for a second time.