I have seen a lot of other commentators bring up versions of this point, but there is a reason why Republicans, especially conservative Republicans, see Newt Gingrich as by far their most qualified nominee and why they have been willing so far to excuse his periodic lapses from conservative orthodoxy.
The reason is simply that under Mr. Gingrich’s Congressional leadership, the Republican Party finally broke the New Deal coalition that had dominated American politics for more than a half-century, moving policy substantially to the right. That is a pretty impressive credential.
The chart below shows the DW-Nominate score for the median member of the House of Representatives dating back to the 1930s. DW-Nominate is a statistical system that evaluates the liberalness or conservatism of a member of Congress on economic policy based on his voting record. Positive scores indicate a more conservative member and negative scores a more liberal one. I have portrayed these as moving in the intuitive direction from left (liberal) to right (conservative) in the chart.

The two large red circles in the chart represent the 104th and 105th Congresses, during which Mr. Gingrich was the Speaker of the House. As you can see, they were associated with an extremely large conservative shift. Part of this is because Republicans had gained 53 seats at the preceding midterm elections and so represented the swing votes in the chamber. But the newly elected Republicans also tended to be quite disciplined in their conservative voting even if they came from moderate districts. The typical Republican member of Congress was more conservative in the 104th Congress than in the 103rd Congress, something that traditionally had not happened when a party does well at an election and expands its coalition.
In other words, Republicans were having their cake and eating it too, winning more seats without having to compromise their conservative principles. This is not to say that Mr. Gingrich’s Republicans never compromised with Bill Clinton and the Democrats — but when they did, they usually won major policy concessions like welfare reform. (The tax increase that Mr. Clinton enacted came in 1993, when Democrats were still in control of Congress and before Mr. Gingrich took over).
What has happened since then? Mr. Gingrich resigned under the cloud of an ethics scandal in 1999. But there was no backlash to speak of; instead, the Republicans’ score card since then has looked pretty good. They have won two of three presidential elections and retained control of the House of Representatives in three of the five elections. And they have continued to move toward the right on economic policy. The current 112th House is probably the most conservative since the New Deal on economic policy.
It is hard to say how much of this shift is because of Mr. Gingrich. Like the quarterback for a winning football team, he is probably given somewhat more responsibility for his party’s wins and losses than he truly deserves. Nevertheless, no other Republican candidate can come close to matching his record. It is also one that older voters in particular — with whom Mr. Gingrich performs extremely well — may be inclined to appreciate. Those older voters may have a keener sense of history and would have remembered that the House of Representatives had been dominated by Democrats for their entire adult lifetimes until Mr. Gingrich came into power.