It's "Mission Impossible" for British prime minister Boris Johnson. Over the next four days, Johnson will have to thresh out a last-minute Brexit deal with the European Union in a summit on Oct. 17 to 18 and have this deal -- if there is one -- approved by the raucous British Parliament on Oct. 19.

If no deal is reached with the EU on Oct. 17 and 18, Johnson is legally bound by Parliament to ask the EU for a delay in the Oct. 31 Brexit departure date. Asking a delay is a task Johnson so loathes he said he'd rather be dead in a ditch than do so back in early September. The odds are he'll do so and reserve his self-immolation for another day.

More optimistic political analysts see a last-minute deal being hammered out since there is word the EU will likely agree to extend the summit until next week to get this job done. Johnson, for his part, is committed to reaching a deal since a No Deal Brexit will likely hasten his downfall as prime minister.

Johnson has pledged to leave the EU on Oct. 31 and has reiterated this pledge to the British public time and again. Johnson's predecessor, Theresa May, failed to achieve in two years what Johnson now has only five days to accomplish.

The success of Johnson's last-minute talks all depends on his last-gasp effort to find a mutually acceptable solution to the largest stumbling block to a Brexit deal -- the  Irish "backstop" issue.

On a technical level, the Irish backstop aims to prevent an evident or "hard" border (or one with customs controls, infrastructure, and personnel) on the border of the Republic of Ireland (an independent state and a member of the EU) and Northern Ireland, which is part of the UK. It's also being called an insurance policy to ensure there is no hard border on the island of Ireland.

Johnson wants to replace the Irish backstop with a system that checks on goods passing between the Republic of Ireland and Northern Ireland. This will remove the necessity of these customs inspections taking place at the border.

The talks starting Thursday will see Johnson try to convince the EU of the soundness of this idea. Ongoing technical level discussions between the EU and the UK, however, aren't taking up this proposed solution. Technical level discussion continued Monday.

The EU has warily received Johnson's proposals. Media reports say the EU is concerned with the legality and technicalities of customs arrangements in Johnson's new proposals.

A statement Sunday from the European Commission stating "a lot of work remains to be done" was no cause for celebration.

Given the still daunting obstacles to a Brexit deal, political experts contend it's unlikely a deal will be reached by the 18th.

"Striking a deal in time for the EU summit on 17-18 October and getting it passed by the U.K. parliament in an extraordinary Saturday session on 19 October poses a huge challenge with a highly uncertain outcome, to put it mildly," said Holger Schmieding and Kallum Pickering, chief economist and senior U.K. economist of Berenberg Bank in a note to investors Monday.

"In addition, the EU may need a technical extension to ratify the deal on its side anyway."

They said their base case is a deal won't be finalized in the next few days and the U.K. will have to ask for a Brexit extension beyond Oct. 31.