The previous debate took place before the publication of the latest international Pisa report, in which Swedish schools performed poorly, with pupils' results falling below the OECD average in a range of subjects.
The results put schools and education at the centre of Swedish politics in 2014, which has been dubbed the "super election year".
"It is hard to avoid jobs, but the school issue has come to the forefront more recently," political science professor Jonas Hinnfors told Swedish Radio News as he listed likely topics for today's debate.
During the debate, Åsa Romson of the Green Party noted that Reinfeldt did not mention the climate once in his opening remarks, while the Left Party's Jonas Sjöstedt said the high unemployment rate is the government's biggest failure. Sweden Democrat Party Secretary Björn Söder said the government has not been tough enough on crime.
Reinfeldt's colleagues in the other three centre-right government parties brought up issues ranging from private businesses in the care sector to Sweden's schools policy and labour migration.
Social Democrat leader Stefan Löfven did not take part in the debate since he does not hold a seat in Parliament. He was replaced by group leader Mikael Damberg. Sweden Democrat Party Secretary Björn Söder stood in for party leader, Jimme Åkesson, who is on paternity leave.