London(CNN) Boris Johnson's job just got even harder.

The UK Prime Minister's first full week in office ended on a very sour note, when one of his own lawmakers was robbed of their parliamentary seat in a special election. Despite a surge for his Conservative party in opinion polls, breathless reports of a "Boris bounce" appear to have been premature.

The Conservatives' share of the vote in the Brecon and Radnorshire region of Wales fell by nearly 10 percentage points, as they came in second behind the pro-European Liberal Democrats. The result leaves Johnson with a working parliamentary majority of just one.

Johnson already faces the toughest challenge of any leader since the end of World War II: to deliver Brexit on October 31 and unite a bitterly divided nation.

Despite all his pro-Brexit rhetoric, Johnson has inherited all the problems that ultimately did for his predecessor, Theresa May. And not having a majority is probably the biggest of all these headaches.

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May famously squandered the slim majority that she inherited from David Cameron, after calling a general election that was intended to boost her power. But her plan backfired, and she was left at the helm of a minority government requiring the support of the hardline Northern Irish Democratic Unionists (DUP).

A working majority of 13 was whittled down over time as the Conservatives lost special elections and lawmakers left the party over what they considered to be May's hard Brexit policy.

It's unlikely these people will be won back by Johnson, who once said that May's approach to Brexit was so soft that it was the equivalent of strapping a suicide vest to the British constitution and handing the detonator to Brussels.

So even with the votes of the DUP's MPs -- who have hardly been reliable allies, refusing to back May's deal three times -- Johnson's majority of one is a disaster waiting to happen. Johnson, let's not forget, has talked an enormous game and made guarantees that could end end his premiership if not delivered.

He has guaranteed Brexit on October 31, "do or die". However, though Parliament has to date been murky about exactly what form of Brexit deal it could back, it's been unequivocal in one thing -- its opposition to a no-deal Brexit.

While there is no single constitutional lever Parliament can pull to prevent Johnson from taking the UK out of the EU without a deal if he is determined to do so, it would set an extraordinary precedent for the executive branch of government (Johnson) to ignore a direct instruction from the legislative branch of government (Parliament). Especially on an issue so crucial to future of the nation.

One option within Parliament's gift is a confidence vote. If Johnson lost such a vote, even narrowly, it would bring down his government, at least temporarily.

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And if you look at public comments made by those Conservative lawmakers who opposed Johnson becoming Prime Minister, it's not hard to see where the rebel votes could come from.

So, just 10 days into the job, Johnson will not be at all relaxed about this by-election result. It might have been expected -- the Conservatives had been behind in nearly every poll running up to the vote. But it knocks the wind out of Johnson's sails and reminds him of the parliamentary nightmare awaiting him in September.

As he considers his fate, perhaps Johnson will reach the same conclusion drawn by Theresa May and attempt to engineer a Conservative majority in Parliament via an early election. It might seem like an act of supreme folly, given what happened to May. But the fact is, when Johnson walked into Downing Street, he did so weaker -- and with fewer options -- than his predecessor.