26 JANUARY: From Independence Day to Republic Day
First, a clarification: the 26th of January was originally declared Independence Day by the Congress Party in 1930, the day being marked by an independence pledge. However, as Indian independence was actually achieved on the 15th of August 1947, the 26th of January became Republic Day instead to mark the day in 1950 the new constitution came into force (although it was actually signed on the 24th of January, 1950).
The reason for choosing the 26th as Republic Day was made clear by Jawaharlal Nehru, Prime Minister at the time, in a message to the nation:
This day links up the past with the present, and this present is seen
to grow out of the past. Twenty years ago we took the first pledge of
independence. During these 20 years we have known struggle and
conflict and failure and achievement.
Yet, undoubtedly, 26 January 1950, is a day of high significance for
India and the Indian people. It does mean the consummation of one
important phase of our national struggle. That journey is over, to
give place to another and perhaps more arduous journey. A pledge is
fulfilled and every fulfilment of a pledge gives satisfaction and
strength for future endeavour.
Cited in Jim Masselos, 'India's republic day: The other 26 January' (Journal of South Asian Studies, vol. 19, 1996)
26 JANUARY 1930: The Original Independence Day
After the Congress Party session in Lahore in December 1929 at which the Poorna Swaraj resolution (complete independence) was passed, the Congress Working Committee members were selected on the 1st of January 1930: Mahatma Gandhi had tight control over who was selected. On the 2nd of January this committee chose Sunday the 26th of January as Independence Day. There does not appear to be any special reason why the 26th of January specifically was selected, but it was probably chosen by Gandhi and seems to have been dictated by circumstances. In an article in Young India dated 16-1-1930, Gandhi wrote:
It was easy enough to pass the independence resolution at Lahore. It
is difficult enough to achieve it even by ‘peaceful and legitimate
means’. The first essential is to let the masses know, understand and
appreciate the message of the Congress. They must know what
independence means and what it is likely to cost. And so the Working
Committee whose business is to make the Congress live in the daily
life of the people has fixed Sunday, 26th instant, as Purna Swaraj
(Complete Independence) Day when a declaration approved by the Working
Committee will be made by those present.
A date earlier than the 26th would have probably have left too little time to prepare the pledge to be read out at planned meetings on the 26th: correspondence between Gandhi and Nehru shows that the pledge was still in the draft stage until at least the 17th of January. Also, as hinted at in the text cited above, time was needed to publicize the event.
Also interesting is the choice of a Sunday. This may have been deliberate, for
Gandhi was not in favour of processions and speeches as he did not
want to precipitate a crisis before he was ready with his plans for
civil disobedience.
Source: Rudrangshu Mukherjee, ‘Nehru & Bose: Parallel Lives’
If Independence Day had been held on a working day, Indians with government jobs would have had to refuse to work on that day if they were to attend meetings for the pledge. Gandhi, though (as noted above), was concerned not to provoke the British before he was ready. If a Sunday was indeed his preferred option, the 19th may have been too soon (see above) so that meant the 26th was the earliest possible Sunday.
This still leaves the question: why not later than the 26th? The answer is most likely that Gandhi was under some pressure not to delay as more radical factions both inside and outside Congress were pressing for action. Independence Day had to be before civil disobedience started and
Gandhi had been authorized by the Working Committee of the Congress to
decide on the timing and the method of the Civil Disobedience
Movement. He chose to do so by marching from his ashram in Sabarmati
to the sea in Dandi to manufacture salt in defiance of the
government’s salt monopoly. He began his march on 12 March with a band
of seventy-one dedicated disciples, and on 6 April he violated the
salt law.
This doesn't rule out a date in, say, early February but, if there was no reason to delay until after the 26th, then why do so?
Sources (in addition to those cited above):
Md. Khairul Anam, 'The Salt Satyagraha Movement, 1930-31' (Proceedings of the Indian History Congress, Vol. 68, Part One (2007), pp. 806-824)
A Centenary History of the Indian National Congress, Vol. 2
K. Tidrick, 'Gandhi: a Political and Spiritual Life'