Trump also said he might speak to former Foreign Secretary Boris Johnson, who quit along with Brexit minister David Davis over May's plans for a business-friendly Brexit which was only agreed by her cabinet last Friday after two years of wrangling.
Earlier in the day, Mrs May was bolstered by the support of senior Brexiteers in her Cabinet.
The opposition is equally as unhappy, with Labour leader Jeremy Corbyn asking on Monday: "How can anyone have faith in the prime minister getting a good deal with 27 European Union governments when she can't even broker a deal in her own cabinet?" She was expected to give a news conference alongside May. We need to see progress beyond this. The British government is due to publish a detailed version of the plans on Thursday.
Interrupted only by a near-death electoral experience when Conservatives lost their majority in parliament in June 2017, May's tenure has been a never-ending party feud marked by frequent and intemperate public statements from several cabinet ministers, especially her now-former foreign secretary, Boris Johnson.
"But I come back to this point, if people don't like this proposal what is their alternative?"
"It is also heartening to see that preparations are being made for a "no deal" Brexit".
"From an Irish perspective, negotiations are key to Ireland's future in terms of the final impact a deal would have on our trade and growth as a country".
He added: "The stance of hard-line Brexiteers is revealing, Boris Johnson's resignation letter to Theresa May in itself reveals actually the degree the type of Brexit he wanted was never going to happen, and he was never really dealing with reality".
"He added life and colour".
"My concern is about the policy, rather than the individual", he said.
In addition to the prime minister's office, the three most critical cabinet positions - Treasury, the Foreign Office and the Home Office - are safely in the hands of those who voted to remain in the EU.
"Over the coming days, weeks and months these negotiations will become more intense as we head towards leaving the European Union on March 29, 2019".
"It is absolutely right that we focus now on these important negotiations to get the best possible deal".
But the chaos surrounding the government will not die down any time soon-the contingent supporting a hard Brexit is more angry than ever.
But Woody Johnson said May had shown strong leadership and that the trip would enhance the special relationship between the United States and Britain.
"In a vote of confidence in the House of Commons I would support the Prime Minister that's because I don't want to have another General Election, there isn't a vote of confidence in either case at the moment, I don't think many people want another election, we only had one a year ago". It would prevent us, probably, from making a deal with America and other countries. But leading pro-Brexit lawmaker Jacob Rees-Mogg said he did not think she would face a leadership challenge. Inside, the paper's report says May finds herself in a "serious crisis" caused by her "inability" to manage an orderly Brexit. Frankly, Putin may be the easiest of them all.