Some 49% of voters surveyed last week by pollsters Civey for Die Welt newspaper said they either "definitely" or "sooner" place trust in Seehofer to solve the perceived asylum crisis compared with 32% who said Merkel has the right approach.
While Merkel would welcome a reprieve from an immediate crisis in her coalition, she is still under intense pressure to deliver a deal with European Union partners who are deeply divided.
In a sign of the frayed nerves, Germany's political and media world lurched into a brief panic Friday as several media outlets fell for a hoax tweet claiming Seehofer's CSU was quitting the coalition.
Europe's migrant situation received worldwide attention last week when Italy and Malta refused to allow a ship with hundreds of migrants aboard to dock at their ports.
German Chancellor Angela Merkel plans to discuss the issue of migration with Italy's new premier on his first official trip to Berlin.More news: Obama Blasts Trump For 'Ripping Children From Their Parents' Arms'
Merkel and Macron have both stressed that, as US President Donald Trump openly challenges the European Union with a trade war and over security and climate policy, the bloc must learn to stand its ground on the world stage.
The calls for tougher policies have come even though the number of people reaching European shores in search of protection has declined.
The EU has given aid and money to countries from Turkey and Jordan to Libya and Niger.
Trump's criticism and Seehofer's insubordination might strengthen Merkel's hand and bring the European Union closer to a common policy on migration and refugees.
U.S. President Donald Trump blamed migrants in Europe for violently changing the culture and for what he inaccurately described as a rise in crime in Germany as he sought on Monday to defend his administration's widely criticized policy on illegal immigration.
But the veteran politicians have often clashed.More news: Meghan Markle's makes an understated Royal Ascot debut in Givenchy
As outlined in his "migration master plan", Seehofer wants to refuse asylum access to German territory if they have already formally entered the Schengen zone via another country.
Merkel is under strong pressure from her conservative allies to take a harder line on migration. "Germany is characterized by Christianity".
Some political analysts have speculated that the CSU manufactured the showdown with Merkel in an attempt to mobilize right-wing voters ahead of critical Bavarian state elections in October. The CSU is traditionally slightly more conservative than Merkel's CDU.
Eurasia Group analyst Charles Lichfield on Monday put the chances of Merkel losing power as a result of the dust-up with the CSU at 25 percent.
Though Merkel had been lukewarm on Macron's idea of a European budget, in a declaration adopted by both leaders following the meeting they said they had agreed upon a proposal to establish one aimed at "competitiveness and convergence".More news: Falling German crime stats "speak for themselves"