Mr Gingrich promises to renew American civilisation, but the weeks since his victory have been notable for radical rhetoric and theatre rather than a coherent political programme.
Changes contemplated by the Republicans include selling off the US Geological Survey - though they hurriedly add that earthquake prediction would remain under government control. Mr Gingrich caused a furore by recommending the virtues of orphanages and even appeared on television with a Danish heart-pump, cheaper than the American one, claiming that its adoption would cut medical costs.
Having underestimated the Republicans before the election, American pundits may now be taking them too literally. There are serious aspects to their "Contract with America" - notably the 50 per cent cut in capital gains tax - but the 10-point agenda was issued on 27 September as a handy package of policies that Mr Gingrich believed would win votes and alienate nobody. It makes no mention of issues on which the Republicans are divided, such as abortion.
The difficulty for Mr Gingrich is the same as that facing any radical in Washington. The division of powers between Congress, the President and the judiciary makes it almost impossible to carry out a full programme. Government institutions in Washington have proved adept at protecting themselves. An issue such as crime - the "contract" has a Taking Back Our Streets Act - is primarily handled by the states, not federal government.
The second limitation on change is that the Republicans have promised not to cut social security or Medicare for the elderly - and have also said they will increase spending on defence. Together with the interest on the national debt, this puts three-quarters of federal spending off limits, while the welfare programme, which Mr Gingrich has talked so much about limiting, makes up just 1 per cent of the budget.
The party's balanced-budget amendment would become law only if passed by two-thirds of state legislatures, many of which fear they will be lumbered with paying for what Washington now funds.
The Republicans know they have promised far more than is feasible to deliver. They also know the dangers - exemplified by President Bill Clinton in the past two years - of disappointing voters by delivering nothing. They need to act quickly in areas where they do have authority by passing into law popular measures such as applying federal laws to Congress itself. Mr Gingrich could also look non-partisan by giving Mr Clinton a line-item veto, stopping members of Congress adding their pet schemes to important legislation which cannot be removed without dumping the whole law.
Much will depend on how Mr Clinton responds to all this. The White House strategy is to give the Republicans enough rope in the hope they will hang themselves. Given the completeness of the Democrats' defeat on 8 November, Mr Clinton does not want to look as if he is frustrating the people's will. More hopefully, from his point of view, Mr Gingrich has shown in the past month - on orphanages and a $4.5m (£2.8m) book deal - that he has flashes of very poor political judgement. As the gloss of his electoral victory wears thin, American voters may not be so willing to let him talk himself out of trouble.
Mr Clinton will also hope that the Republican leaders will fall out among themselves as they vie for the 1996 presidential nomination.
Last week Senator Bob Dole did little to mute his criticism of Mr Gingrich over his agreement to write the book.