If they brought him a Shofar or Lulav on the first day during Bein Hasmoshos*, then according to all opinions he should do the Mitzvah without a blessing – because now the doubt is with regard to his very obligation to fulfill the Mitzvah.

[*Bein hasmoshos is a period between day and night before it gets completely dark. We are uncertain whether legal nightfall is at the beginning, end, or sometime during this period. The Mitzvos of Shofar and Lulav can only be done during the day. — JC]

However this is not so, because the timing of the [Mitzvah] of Remembering the Exodus from Egypt [mentioned in the third paragraph of the Shema] extends further, as stated by the Magen Avrohom later in Siman 70, so he is still duty bound to say at least the blessing of ‘It is true and certain’ [the blessing after the Shema, which refers to the Exodus] until a third of the day as mentioned in Siman 58. After this time [when one can no longer say this blessing,] they did not institute a blessing for this Mitzvah, but out of doubt one should still say a verse mentioning the Exodus from Egypt – Shaagas Aryeh Siman 10.

It says in Tractate Brachos 13b that if one said a law in which the Exodus of Egypt is mentioned you have fulfilled this Mitzvah. The Magan Avrohom writes: It appears to me that all the more so if one said the ‘Song at the Sea’ that he has fulfilled the Mitzvah. The Chasam Sofer disagrees because of the verse “in order that you shall remember the day of the Exodus etc” i.e it is inadequate just to mention that they crossed the sea [without stating that they left Egypt]; and the Gaon R’ Akiva Eiger agreed with him.

The idea of fulfilling the Mitzvah of remembering [the Exodus] by thinking about it [as opposed to actually saying the words] is discussed in the Be’er Heitev in the name of the Beis Yaakov. The Pri Megadim is doubtful about this, and the Shaagas Aryeh in Siman 13 goes to great length to find a proof in the Talmud, and concludes that one has not fulfilled his duty.

It is obvious in the Talmud that at night one must also make mention of the Exodus from Egypt. The Pri Megadim discusses whether this is a Torah ordained duty or a Rabbinical enactment – the difference would be if one is in doubt. The Shaagas Aryeh in Siman 8 writes explicitly that this is a Torah law. One is obligated to mention the Exodus at a time that is definitely night and not earlier; therefore, if one mentioned it during Bein Hashmoshos, e.g if he prayed the Evening Service before nightfall, he has not fulfilled his duty because Bein Hashmoshos is a doubtful period (see above) and with regard to a doubt in a Torah law one must be stringent. And the Rambam in Chap. 1 of The Laws of the Shema also implies that it is a Torah law as the Pri Megadim himself wrote.

It would seem that if he knew that he said the first verse or the first paragraph, ie he said that which is Torah Law according to each of the different views [above] and he is only in doubt about the rest, that he need not repeat it. However, in Siman 64:3-4 it appears that one should repeat it – this must have been the original institution, to repeat it. Where one is in doubt if he said the third paragraph and “Emes V’Yatziv” [the following blessing, ‘It is true and correct’], then he must repeat it because all agree that mentioning the Exodus is a Torah law. [The third paragraph of the Shema incorporates the Mitzvah of Wearing Tzitzis on a four cornered garment as well as the Mitzvah of Remembering the Exodus of Egypt. — JC] However there are various opinions about this as well. Some say that one should say the third paragraph and also ‘It is true and correct’, because it is all one item. Others say that he should just say the third paragraph and thereby fulfill his Torah obligation, and he need not say ‘It is true and correct’ – and so agreed the Shaagas Aryeh.

The Shaagas Aryeh also wrote that if this doubt occurred in the evening, when one does not know if he said the third paragraph and “Emes V’Emunah” [the first blessing following the Evening Shema, ‘It is true and faithful’], then he should repeat ‘It is true and faithful’ and he need not repeat the third paragraph of the Shema. [There is no obligation to wear Tzitzis at night – JC]. If he is certain that he said all three paragraphs and is only in doubt about ‘It is true and correct’ in the morning or ‘It is true and faithful’ in the evening, then the rule is the same in both cases: that he need not repeat it. This is because since he said the third paragraph and thus made mention of the Exodus, according to all views the blessing is merely Rabbinical.