As battles over Britain's final Brexit proposals continue to cause divisions within Theresa May's government and the U.K. parliament, support for the British prime minister and her leadership is coming from an unlikely source — Europe. Divisions between so-called 'Brexiteers' and 'Remainers' are rife in the U.K.'s parliament, with battle lines drawn between politicians who favor a hard separation from the rest of the European Union, and those that want a "soft" Brexit in which the U.K. stays roughly aligned to Europe in terms of trade and regulations, making a post-Brexit relationship easier. Stuck between these warring factions, Prime Minister May has erred towards the latter, aiming for a softer divorce from the bloc. Outlining her plans for the U.K.'s relationship with the EU after March 2019, May's "Chequers plan" shows her favoring close regulatory alignment with the EU's single market in order to facilitate trade after Brexit.

Tthe President of the European Commission Jean-Claude Juncker embraces the Prime Minister of the United Kingdom Theresa May on June 28, 2018 in Brussels, Belgium. Thierry Monasse | Getty Images News | Getty Images

Setting out such an arrangement is the easy part, however, with the other 27 EU members having to approve any final deal, as well as members of the U.K. parliament having to approve any final Brexit deal, also known as the "withdrawal arrangement." Although a group of Brexiteers have mounted a challenge to May's plan, other members of parliament have rallied around her. For her part, May has said it's her deal, or "no deal." Christopher Peel, chief investment officer at Tavistock Investments, told CNBC that the next few weeks would be critical in the Brexit timeline. "Both sides of the U.K. political divide remain split on their version of Brexit. Theresa May has struggled to find a common ground, but she will probably survive long enough to see out the negotiating process to its conclusion," Peel said Wednesday.

Hard sell

With the clock ticking and the March 29 exit date drawing near, both the U.K. and EU want to have a deal on their future relations in place by the time a two-day summit happens in mid-October. Outstanding issues yet to be resolved include trade and security and — perhaps the biggest stumbling block — the border between Ireland and Northern Ireland that will become the U.K.'s land border with the EU after Brexit. Ironically, May's Brexit plan is turning into a harder sell at home than it is in the EU. Many pro-Brexit politicians at home are rebelling against May's deal, saying it does not allow the U.K. to strike out on its own to forge its own trading relationships with the rest of the world. Many of these MPs are threatening to oppose the Chequers plan in any final vote, as have the opposition Labour party. "May has got in the middle between negotiating on behalf of the U.K. with Europe and her own party, which is basically trying to get rid of her, or threatening to get rid of her at every step, so it's a kind of 'muddle-through' (situation) for Brexit," Kieran Calder, head of Equity Research, Asia at Union Bancaire Privee, told CNBC on Thursday.

Theresa May, U.K. prime minister, left, shakes hands with Jean-Claude Juncker, president of the European Commission, ahead of a meeting at the European Commission building in Brussels, Belgium, on Monday, Dec. 4, 2017. European Union chief negotiator Michel Barnier told European lawmakers that a breakthrough is likely on Monday in Brexit talks as May arrived in Brussels. Dario Pignatelli | Bloomberg via Getty Images

Meanwhile, in the EU, national leaders appear to be aware of how fragile May's position is, and consequently appear to have mollified their position towards her — or at least look like they will try to meet her halfway. All eyes are on Salzburg in Austria where May met her EU counterparts on Wednesday evening and Thursday. Ahead of the summit, May called on EU leaders to drop "unacceptable" demands in the Brexit negotiation. She will need all the goodwill and support she can get from leaders there though several have signaled their willingness to compromise. Nonetheless, the real drama — and battle lines — are at home for May. "While this (the summit in Austria) suggests a focus on the negotiations between the EU and the U.K., the process is by now occupied mainly with selling the eventual deal at home in Westminster," Carsten Nickel, deputy director of research at Teneo Intelligence, said in a note Tuesday. "There is still no serious discussion about the all-important withdrawal agreement in the U.K. Instead, May's Tories continue to fight over the Chequers plan which will, in reality, never see the light of the day. As a result, decades of an intense and mostly theoretical discourse on Europe will come to a head within just a handful of days, once the eventual deal forces every individual MP to decide how to cast their vote," he added. Nickel said that while support for a deal should still be the base case, "the risk of rejection remains very real," at 40 percent.

The Northern Ireland factor

The Northern Ireland border issue is perhaps the most divisive and politically toxic element to Brexit discussions. There is little political appetite to see Northern Ireland treated differently to the rest of the U.K., despite the fact it is set to become the U.K.'s only land border with the EU and there is a strong desire on both sides to keep goods and people moving freely between the countries without a "hard" border.

Traffic crosses the border into Northern Ireland from the Irish Republic alongside a Brexit Border poster on the Dublin road Co Armagh border, between Newry in Northern Ireland and Dundalk in the Irish Republic, on December 1, 2017. PAUL FAITH | AFP | Getty Images