She is hoping to bring back a tweaked divorce accord for a vote, which could come as early as next week but may not take place until March 12.
Cabinet Secretary Mark Sedwill told a parliamentary committee that the TV spots will be aired in advance of Britain's scheduled departure from the European Union on March 29.
Any extension would need to be approved by all 27 other European Union leaders.
Ahead of Wednesday's debate, Chancellor Angela Merkel discussed Brexit during a meeting with President Emmanuel Macron in Paris.
Merkel said: "If Great Britain needs more time we will not oppose it but of course we are seeking an orderly exit".
Her amendment therefore contained May's commitment on giving MPs a vote on delaying Brexit if both her deal and no-deal are rejected by MPs.
Her U-turn on Tuesday prompted outrage among hardliners in the ruling Conservative party, with influential anti-EU MP Jacob Rees-Mogg warning that "any delay to Brexit is a plot to stop Brexit".
While momentum for a second referendum has grown in recent months - and advocates swarmed Westminster today - it's not clear how many MPs actually want a do-over. If Britain leaves with a deal, there will be no change until at least the end of 2020.
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The video appears to show the approach to the airport before the flight diverted to Malaga-Costa del Sol. Another commented: "Omg, glad I was not sat on that".
During Wednesday night's votes, MPs rejected a Scottish National Party (SNP) motion saying the United Kingdom should not leave the European Union without a deal "under any circumstances" by 324 votes to 288.
It calls on the government to make efforts to preserve the rights of those expats set out in the divorce agreement, even in a "no deal" scenario.
"We continue to see the most likely outcome of the current impasse as eventual ratification of the prime minister's Brexit deal, with a three-month extension of Article 50", Goldman Sachs said.
"That such an amendment is needed is in itself a very sad state of affairs", said Alberto Costa, the Conservative lawmaker behind the motion.
Opposition to the Brexit deal, agreed in November after nearly two years of negotiations between London and Brussels, is focused on the so-called backstop plan to avoid checks on the Irish border.
Labour leader Jeremy Corbyn dramatically shifted his own position on Brexit this week by opening the door to backing a second referendum.
Lawmakers also rejected a proposal on Wednesday by the Scottish National Party calling for a no-deal Brexit to be ruled out under any circumstances.
Twenty Tories, including Esther McVey, the former work and pensions secretary, voted against a government-backed amendment laid by Yvette Cooper, the former Labour minister, and created to pin Mrs May to her pledge to give MPs the chance to delay Brexit.
Any public vote would "offer the British people a choice between a credible "Leave" option endorsed by this house, and the option of staying in the EU", he said.