Mr Schmitt's resignation could even help Mr Orban in his rows with Europe over media freedom.
Mr Orban has said he is ready to co-operate to dispel such worries about the constitution.
But the Hungarian Prime Minister Viktor Orban has said that human error was "more than likely".
At least in the short term, time and events are not on Mr Orban's side.
Until now, the only body to have kept Mr Orban at bay was the central bank.
Mr Orban has been given a month to make changes to the controversial laws.
But the newly-elected Prime Minister Viktor Orban decided not to renew the standby facility last year.
That will strengthen the whiff of Putinism that some already scent around Mr Orban's government.
Since Hungary's election in April put the hard-edged Viktor Orban in power, it is payback time.
Where, ask Mr Orban's supporters, were outsiders when Hungary was run by sleazy and rapacious ex-communists?
Leonard Orban, who was in charge of Romania's accession negotiations, will become a commissioner.
Ronald Lauder, president of the World Jewish Congress, asked Orban to confront "dark forces" such as Jobbik.
Mr Orban also said there would be "very severe" consequences for those to blame for the disaster.
Before the vote, Hungarian Prime Minister Viktor Orban accused the EU of interfering in Budapest's domestic affairs.
He said he would discuss the issues of concern with Mr Orban on 24 January in Brussels.
It marks a remarkable change in Hungarian politics: Mr Orban is turning the right into a mass movement.
Mr Orban's cabinet says the reforms are necessary to cut spiralling spending and also boost low employment rates.
She was the only person on the policy board who was not appointed by either Mr Orban or Fidesz.
Yet on a recent visit to London Mr Orban was in robust mood.
Many protesters sported painted faces and clowns' noses after Mr Orban's alleged remark.
The opposition, led by the mercurial and opportunistic Viktor Orban, is little better.
But protesters are now particularly angry that the Mr Orban's government has abolished their retirement rights retroactively, our correspondent adds.
In a written response to Mr Barroso's telephone call, Mr Orban said that Hungary was "fully committed" to European standards.
Indeed, in Viktor Orban, Hungary's aggressively right-wing prime minister, Mr Klaus may have Central Europe's nearest thing to a soulmate.
The prime minister, Viktor Orban, often points out that Mr Milosevic tends to pick on ethnic minorities one by one.
Mr Orban says the changes are necessary in order to complete the work of eradicating the legacy of Communism from Hungary.
"If you have slept, you use a means of navigation that is less thoughtful, " Mr Orban told the BBC News website.
At least 100, 000 people have rallied in Hungary's capital Budapest in support of embattled Prime Minister Viktor Orban and his government.
BBC: Thousands of Hungarians rally to back embattled PM Orban
This was a massive show of support for Mr Orban and his Fidesz government, the BBC's Nick Thorpe in Budapest reports.
BBC: Thousands of Hungarians rally to back embattled PM Orban
No matter, Mr Orban, unabashed, is backing a referendum initiative aimed at preserving ballot papers so that they can be recounted.
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