Boris Johnson and Jeremy Hunt both vowed to ditch the contentious Irish border backstop as they faced questions from Conservative Party members in Northern Ireland.
But what exactly is the backstop and why is it creating such a logjam in the Brexit process.
What is the backstop?
It is effectively an insurance policy written into the withdrawal treaty that will ensure, come what may in future trade talks, that the Irish border will remain free flowing post-Brexit.
Activated if a wider trade deal fails to materialise before the end of the Brexit implementation period, the backstop would see the UK enter into a temporary customs union with the EU for an indefinite timeframe, to avoid the need for customs checks on the 208 crossings along the 310-mile frontier.
In addition, it would also see Northern Ireland adhere to EU single market rules on goods, to rule out the need for regulatory checks on products and livestock crossing the border.
Why is it needed?
For the EU, and the Irish Republic in particular, the backstop was a fundamental requirement of any exit deal struck with the UK.
While the shape of the future relationship was to be hammered out in phase two of the negotiations, Brussels and Dublin demanded the mechanism in phase one, to guarantee the border would always remain open, regardless of what the future held.
Their case was economic and political.
They argued that any customs or regulatory border would have a devastating impact on the economy of the island.
A UK Government mapping exercise has detailed 142 different areas of cross-border life in Northern Ireland that could be impacted by the UK’s exit from the EU, from trade to healthcare.
The EU is also determined to protect the integrity of the single market, amid fears an open land border with the UK could see goods which do not meet Brussels’ regulations into the 27 member states.
But the Irish border is much more than a trade crossing.
It is a highly sensitive political construct, a physical manifestation of the constitutional dispute between nationalism and unionism.
Heavily fortified during the Troubles, and often the scene of bloodshed, the border has become almost invisible since the peace process – with people and goods moving freely between north and south.
Despite differences on many things, there is almost universal political consensus across the island that any return to checkpoints on the border would be a backward step, with police chiefs north and south warning that the erection of physical infrastructure could prompt an upsurge in dissident republican violence.
Why are many Brexiteers opposed to the backstop?
They fear the backstop could lock the UK into a customs union with the EU, preventing it from striking lucrative new trade deals and fulfilling the promises of the 2016 referendum.
They insist the mechanism gives the UK no unilateral way of exiting the backstop, without the approval of the EU.
In regard to the different arrangements in Northern Ireland, Brexiteers also fear the backstop will undermine the constitutional integrity of the UK by erecting economic borders down the Irish Sea.
The DUP, the Conservatives’ confidence and supply partners at Westminster, is vehemently opposed to backstop.
For the DUP, the Union of Great Britain and Northern Ireland comes above everything.
The party could potentially stomach the mechanism if it was time-limited or if the UK could pull the plug when it wanted.
The withdrawal agreement contains neither provision, with the backstop theoretically remaining in place “unless and until” alternative arrangements are found.
So has anyone found these any alternative arrangements?
Brexiteers believe they have.
They insist it is possible to have divergent regulations and different tariff regimes and yet still keep the border open.
The key, they contend, is through the use of technology and light-touch monitoring conducted away from the border.
Proposals include trusted trader schemes and advanced use of data and IT systems.
The Government has established a number of expert panels to examine these so-called alternative arrangements while a group of Brexiteer MPs set up their own commission to look at the issue.
Among its recommendations, the Alternative Arrangements Commission proposed forming a new UK/Ireland single zone for food standards.
There is widespread scepticism among EU leaders whether any technology solution exists that could effectively keep the 200-plus road crossings flowing freely, particularly when it comes to the movement of animals and food products.
Brussels has committed to exploring alternative arrangements in talks on the future relationship, but only if the backstop is agreed up front.
And therein lies the current Brexit conundrum.