The caller, named as Laura from East Dulwich, said to Nick Clegg: "I'm just wondering why the coalition is discriminating against mothers like me who care for their children at home, with the latest announcements?"
Arsene Wenger has suffered a difficult few days with his team getting knocked out of the FA Cup, having an angry exchange with journalists at a press conference and seeing his Arsenal side lose to Bayern Munich last night.
But the French manager has received some unlikely support from the Deputy Prime Minister Nick Clegg.
The Liberal Democrat leader and Gunners fan was asked on LBC Radio what he thought of Arsenal's defeat last night and said: "I'm heartbroken ... I know what it's like to lead a team through ups and downs."
He added: "The guy (Wenger) has achieved amazing things in 16 years and he has got an incredibly young and talented team ... to now start all blaming it on him, I think might make things worse at Arsenal."
When Nick Clegg was told that Boris Johnson was no actually on the line, but had pre-recorded his message, the Deputy Prime Minister responded: "That's easy for him, isn't it?"
Boris, if you're listening - and I suspect he isn't - I think we have actually cut the amount of taxpayer money which is used to pay for the cars and everything for ministers by, I think, about 70%. We have massively slashed it and changed it.
Clearly, ministers - myself included - drive in cars, but not all the time. I am about to jump into a train to go up to Sheffield this afternoon.
I think the fact we have cut the bill we inherited from Labour for ministerial cars by, I think, around 70% is a big step in the right direction."
London Mayor Boris Johnson ambushed Nick Clegg on his radio phone-in, urging him to get his Cabinet colleagues "out of their posh limos" and on to public transport.
Mr Johnson recorded a message for LBC 97.3 radio to demand more spending on London's transport system.
Hi Nick, it's Boris here from Islington.
I just want to ask you when are you going to get all those Government ministers out of their posh limos and onto public transport like everybody else?
How can we possibly expect Government to vote for increases in infrastructure spending which we need in this city and upgrading the Tube, which we all need, when they sit in their chauffeur-driven limousines - paid for by the taxpayer - rather than getting down on public transport with the rest of us?
Nick, get them out of their limos! Boris, over and out.
But Mr Clegg, appearing on his weekly phone-in show, insisted the coalition Government had cut spending on ministerial cars by around 70% and challenged the Conservative Mayor in his turn to make use of billions of pounds worth of Treasury guarantees for infrastructure projects.
Nightclub owner Peter Stringfellow could stand against Nick Clegg at the 2015 general election after the Deputy Prime Minister twice singled him out as someone who did not deserve state-funded pensioner benefits.
He said that at 72 he had "done everything a guy would probably like to do... and I might take a serious view of moving into politics", with his home town of Sheffield the most likely target.
In his weekly phone-in show on radio station LBC 97.3, he was asked whether he might stand in Mr Clegg's Sheffield Hallam constituency. He said: "I think 'why not?'. It has opened my mind to the possibility and the idea of going back to my home city and taking him on would be my first choice."
The deputy prime minister Nick Clegg will be braving calls from the public this morning as part of a new weekly radio phone-in. The Lib Dem leader will be on LBC at 9am every Thursday, starting from today. Some are seeing it as a bid to boost his popularity.
It will be the first time such a senior government figure has agreed to a weekly grilling by listeners.Mr Clegg said: "I'm doing this because I don't think politicians get to hear enough from people directly."
"You can't do the right thing in government unless you keep in touch with how people are thinking and feeling."
His first phone-in comes in the week of the Government's Mid-Term Review, which was seen as an attempt to relaunch the coalition at the halfway point in its planned five-year term.
But the initiative was plunged into chaos after it emerged an audit of the coalition's record in power had not been published.It only came to light when one of the Prime Minister's aides was spotted carrying a document which suggested publication had been delayed to avoid unfavourable coverage.