James D. Morgan | Getty Images Entertainment | Getty Images

Brexit might be changing the course of British and European history but that hasn't stopped Americans from taking an interest — and having a say. President Donald Trump has been characteristically forthright, commenting on both the opportunity that leaving the 28-member union could bring to the U.K. and U.S.' relationship, and also on how badly he thought British Prime Minister Theresa May had handled the negotiations. Brexit faced a crucial week this week as May tried to get her Brexit deal approved by the U.K. Parliament. It failed to win enough support from British lawmakers for a second time but MPs also then voted to reject the option of leaving the EU without a deal. They are next going to vote on whether to delay Brexit altogether. WATCH: Niall Ferguson: Brexit has turned into a student asking for a paper extension

Confused? We all are. In fact, it's a bit of a mess in a country known around the world for formality, order and protocol.

What do Americans think?

Americans could be forgiven for thinking Britain has gone a bit potty (that is, mad) over Brexit — so CNBC asked members of the public in New York what they know and feel about the whole Brexit process.

I think it's pretty terrible. I think the Brits were lied to (and tricked) into voting for something they had no idea about and I think they got themselves into a mess because they were lied to. Todd Peterson Bryant Park, New York.

Todd Peterson said Brits were lied to "about the whole idea that Brexit was supposed to be this wonderful thing — the whole idea about the payments to health care — none of them were true. It's hard to tell (how it will play out)." It's an opinion shared by others. "It's uncertain right now, it seems like it's up in the air after the recent vote" to reject the Brexit deal, Lane Campbell told CNBC Wednesday. "They just don't have the political will to pull this together. There's a lot of uncertainty and it's hurting their economy for sure ... And considering the banking sector — I hear a lot of it is moving to Germany. Hopefully they can do it or not do it but they need to decide," he added. Dmitry Chirun, a U.S. resident for 12 years and originally from Belarus, told CNBC that Brexit was damaging the U.K.'s economic reputation. Brexit "has produced less economic incentives right now for people to work with the U.K. compared to the past when it was integrated into the EU," he said.

LONDON, UNITED KINGDOM - FEBRUARY 13: Anti-Brexit supporters protest outside the Houses of Parliament in London as they call on MPs to rule out a no deal Brexit and demand a People's Vote on EU membership on February 13, 2019 in London, England. Wiktor Szymanowicz | Barcroft Media | Getty Images

A big part of problem surrounding Brexit in the U.K. — and no less for May — is that there are so many opposing opinions on the issue and no consensus over what a future relationship should look like. Protests by the public have become commonplace outside the Houses of Parliament in London, while inside the building May's government has been torn between warring factions. There are those within her party, and the opposition, seeking a "softer" Brexit and maintaining close ties with the EU. And so-called euroskeptics within her party and the allied Northern Irish Democratic Unionist Party (DUP) who want a "harder" departure and a more separate U.K. that can quickly strike free trade deals around the world. The fact that Brexit has proven so divisive in the U.K. (and still causes many family arguments around the dinner table) is not lost on people in New York. "I think people aren't comfortable one way or another (with Brexit) and you've got the generational differences as well. So I think there needs to be more dialogue so that people understand both sides of the equation and then they can come to something that's good for everyone involved," Nina Ahuja, a Canadian tourist, told CNBC.

I think people aren't comfortable one way or another (with Brexit) and you've got the generational differences as well. Nina Ahuja Canadian tourist

Two years of talking about Brexit don't seem to have brought Brexiteers and Remainers any closer to each other, however, although most lawmakers (and the British public) want a deal rather than a no-deal exit. The 2016 referendum on EU membership polarized the country with London, Scotland and Northern Ireland voting heavily in favor of remaining in the EU, and the rest of England and Wales wanting to leave or "sitting on the fence." Needless to say, the British public and EU are both exasperated with the political establishment in London as the impasse continues. "I've been following the story for a little bit and it doesn't seem like people agree on (Brexit). They voted for Brexit but no one actually thought about what it would look like and no one can agree on what they want," Nikku Chatha, a New Yorker raised in Baltimore told CNBC.

America First

As his own election victory in 2016 was seen as a result of populist, anti-establishment sentiment, Trump has appeared an ardent supporter of the concept of Brexit. In May 2016 ahead of the referendum, Trump said the U.K. would be "better off" without the EU and when a majority of Brits indeed voted for Brexit in June, he hailed it as a "great victory." He drew a parallel between the result and Brits wanting "their country back" and his candidacy for the White House.

One member of the public we met in New York told CNBC that he also saw parallels between Brexit and Trump's rise to power. "There's a backlash in America, I think we're seeing it in the Republican Party these days against being part of a global economy. So I'd say that similar populist forces are happening in both countries. And for many British people I'd imagine that the European Union is an easy target when the overall economy is bad," Chatha said. Showing their different perspectives on Brexit, Trump promised the U.K. a "great" trade deal after Brexit whereas his predecessor Barack Obama had warned that Brexit would put Britain "at the back of the queue" for trade talks.

President Donald Trump and the First Lady Melania Trump are met by Britain's Queen Elizabeth as they arrive for tea at Windsor Castle in Windsor, Britain, July 13, 2018. Kevin Lamarque | Reuters

Since the U.S. election in November 2016, Trump has tried to offer May negotiating advice, reportedly telling her to be "tough" and "brutal" during talks and then criticizing her last year for not taking his advice. Then, when the U.K. and EU published the Brexit deal they had agreed last November, Trump was damning, saying it was a "great deal for the EU." The U.S. has a trade surplus with the U.K. and is unsurprisingly keen to maintain the status quo in an era when it is acutely aware of its trade deficit with other trading partners.

U.S. goods and services trade with U.K. totaled an estimated $231.9 billion in 2017 and the U.S. goods and services trade surplus with U.K. was $14.2 billion in 2017, according to the Office of the U.S. Trade Representative. From the U.K.'s point of view, the U.S. is the country's biggest individual country trading partner but the 28-member union is the U.K.'s biggest trading partner as a bloc. In 2017, the EU accounted for 45 percent of U.K. exports of goods and services and 53 percent of imports. But in terms of individual countries, the U.S. was the U.K.'s largest trading partner in 2017. In that year, the U.K. exported £112 billion ($148 billion) of goods and services to the U.S., equal to 18 percent of all U.K. exports.

In contrast, the United States has a widening trade deficit with the EU. Just in terms of goods, the U.S. trade deficit with the entire EU was $146 billion in 2016 and this rose to $169 billion in 2018, data from the U.S. Census Bureau show.

Magical thinking

As the deal stands, the U.K. cannot pursue independent free trade deals during the 21-month transition period (that will only kick in if there's a deal). The U.K.'s pro-Brexit Trade Secretary Liam Fox had been confident in 2017 that the U.K. could replace up to 40 free trade deals with more than 70 countries that the EU currently has in place with its own deals on Brexit day (March 29). So far, it has so far only signed a handful of "continuity trade agreements" to preserve current trading arrangements during the post-Brexit transition period, including one with the U.S. But these are not free trade deals (which it cannot sign as an EU member now and during the transition period). Trump is not alone in criticizing either the deal or the U.K. government's approach to Brexit.