It is a sensitive debate in Germany, where guilt over World War II and the Holocaust has created a strong pacifist tradition, but which has been under pressure, and increasingly committed to, playing a greater security role matching its economic strength.
Washington has long urged NATO allies to spend more on collective defence, but Trump sharpened the tone when he branded the alliance "obsolete" and accused European members of getting a free ride while the US provides 70 percent of spending.
US Vice President Mike Pence stressed this week in Brussels that "the president expects real progress by the end of 2017".
Firmly in the crosshairs of Trump's challenge is Germany, the top EU economy, which runs a trade surplus with the United States and just reported a public budget surplus of €24 billion for last year.
Merkel has reiterated that Germany remains committed to raising military spending from 1.2 percent of gross domestic product now to two percent by 2024, in line with commitments made at a 2014 NATO summit in Wales.
But while this remains the agreed goal of both Merkel's centre-right CDU and the centre-left Social Democrats (SPD), there is discord about how quickly Germany must rush to achieve the target and heed Trump's stern demand.
'Arms spending spiral'
"Even in an election period, we must remain realistic," said new Foreign Minister Sigmar Gabriel of the SPD, adding that meeting the goal now would cost Germany 25-30 billion euros a year.
Gabriel warned against an "arms spending spiral" and cautioned that more weapons do not necessarily equal more security.
So far, of the 28 NATO members, only the United States, Britain, Poland, Greece and Estonia meet the two percent target.
At last week's Munich Security Conference, Gabriel questioned whether it was a good idea for debt-stricken Greece to reach the target "when they can't pay pensions" and asked whether this really will "improve stability in Greece".
Such comments put the SPD at odds, at least in tone, with Merkel's party, to which it still serves as junior partner in a coalition government.
On Tuesday, Merkel's government announced it would boost the armed forces' troop strength to almost 200,000 by 2024.
"The Bundeswehr has rarely been as necessary as it is now," said Defence Minister Ursula von der Leyen.
"Be it in the fight against Isis terrorism, the stabilisation of Mali, the ongoing support of Afghanistan and against people smugglers in the Mediterranean and the Aegean, or with our increased presence for NATO in the Baltics."
Von der Leyen has been a chief proponent for Germany to evolve from "political dwarf" traumatised by the Second World War, to an increasingly central military player in Europe.
Germany has been willing to send troops abroad under two conditions - that the mission is approved by parliament and takes place within a multinational alliance such as the UN, NATO or the anti-Isis coalition.
Defence vs aid
The SPD's top candidate, Martin Schulz - who has pledged to unseat Merkel in September elections and has narrowly beaten her in three recent major opinion polls - has so far remained rather silent on the question of defence spending.
But Gabriel's comments, and Schulz's previous speeches, signal the SPD will push social welfare over unpopular military spending, an approach that could help it claw back its traditional left-leaning voters.
Conservative daily Frankfurter Allgemeine Zeitung characterised such an approach as irresponsible, saying in an editorial that "building kindergartens is more popular, but our army needs to grow".
Merkel, as chancellor and candidate, has characteristically stuck to her "middle path" approach.
While she has reiterated the pledge to reach two percent by 2014, she replied to a journalist's question on boosting spending now: "You are talking about the defence budget, let's talk about the aid budget."