The test for David Cameron in his first full-scale reshuffle was to prove whether he was "a man or a mouse." It was set last week by Tim Yeo, the former Environment Minister, who challenged the Prime Minister to have the courage to drop his previous opposition to a third runway at Heathrow Airport.

Mr Cameron passed the Heathrow test by shunting Justine Greening out of the Department for Transport after only 10 months. Yesterday's Cabinet shake-up was also a wider "man or mouse" test for the PM, who has looked increasingly weak in the face of mounting criticism from his rebellious, independent-minded MPs, many of whom hate the Coalition and are retrospectively punishing Mr Cameron for not winning an overall majority in 2010.

There was plenty for the Tory traditionalists to cheer in what will be seen as a lurch to the right.

Nick Clegg chooses Liberal Democrat ministers but does not have a veto over Tory appointments. He would have preferred Kenneth Clarke (dubbed "the sixth Lib Dem Cabinet minister") to stay at the Ministry of Justice and for Ms Greening to remain at Transport, and will not be overjoyed that Owen Paterson, a right-wing climate change sceptic who opposes wind farms, is taking over the environment brief. Michael Fallon, a hard-nosed and experienced operator, has been installed at Business, to try to impose pro-business, pro-growth policies on Vince Cable, who is reluctant to reduce employees' rights.

Despite the constraints and frustrations imposed by coalition, the Prime Minister was exerting his traditional authority. "He hopes it will galvanise the troops," one Cameron ally said last night. It will certainly please the Tory right, which has been urging the PM to stand up to Mr Clegg.

Aides insist Mr Cameron promoted the best people for a new phase of delivering reform. But they don't deny a tilt to the right, saying Mr Clegg could not expect Mr Cameron to appoint liberal Tories in every department.

The reshuffle may stabilise his party for a while, but there could be trouble ahead. Stroppy Tory backbenchers will expect the shift to the right in personnel terms to be matched by a parallel shift in policies. The two Coalition parties were always going to diverge ahead of the 2015 election. A lot of tricky policies will soon be marked "manifesto territory" and they will go their separate ways.

But if the newly appointed Tory ministers try to push through a raft of right-wing measures before the election they will face opposition from the Lib Dems, who do have a veto on policy if not people. Policies still have to be signed off by Mr Clegg; the reshuffle does not magically create a Commons majority for the Tories, however much they might wish otherwise.

The danger for Mr Cameron is that yesterday's shake-up is seen as his departure from his modernising project. If the Conservatives are seen as the "nasty party" again, that could open up a gap in the market for the Lib Dems, who will target "soft Tories" after losing many progressive voters. Mr Cameron may need to appeal to his own party now, but in 2015 he will need to appeal to the whole country.