The Gemara in Masechet Berachot (10) concludes that Halacha follows the view of Rabbi Yehoshua, who held that the final time for reciting the morning Shema is the end of the third Halachic hour of the day. However, the Gemara adds that this deadline does not apply to the Berachot which we recite before and after Shema. The Berachot may be recited past the third hour, and thus even if one neglected to recite Shema before the end of the third hour, he may still recite the Berachot. The Gemara does not specify until precisely what point in the day one may recite the Berachot, and simply says, "Mi’kan Va’elach Lo Hifsid" ("after then, he has not forfeited [the Berachot]").
We find three different views among the Rishonim (Medieval Halachic scholars) regarding the question of until when one may recite the Berachot of Shema. The Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204) and Rif (Rabbi Yishak of Fez, Morocco, 1013-1103) maintained that one may recite the Berachot the entire day, until sundown. The Ritba (Rabbenu Yom Tob Ben Abraham of Seville, Spain, 1250-1330) and some of the Tosafists (Medieval French and German scholars) held that one may recite the Berachot only until Hasot (midday), whereas the Rosh (Rabbenu Asher Ben Yehiel, Germany-Spain, 1250-1327) ruled even more stringently, claiming that the Berchot must be recited by the end of the fourth Halachic hour.
The Shulhan Aruch (Orah Haim 58) follows the stringent position of the Rosh, and allows one to recite the Berachot of Shema only until the end of the fourth hour. This means that one has only one Halachic hour past the final time for Shema to recite the Berachot. However, with regard to the Berachot, one may rely on the later of the two calculations of the final time for Shema. The calendars generally post two different deadlines for the morning Shema recitation, reflecting the different calculations of the Magen Abraham (Rabbi Abraham Gombiner, Poland, 1637-1683) and the Vilna Gaon (Rabbi Eliyahu of Vilna, 1720-1797). With regard to the Shema recitation, one should endeavor to follow the stringent view, and recite Shema before the earlier of the two times. When it comes to the Berachot, however, one may follow the later of the two times in determining the end of the fourth Halachic hour.
If one did not recite the Berachot of Shema by the end of fourth Halachic hour, then he may no longer recite them that day.
Summary: Although the morning Shema must be recited by the end of the third Halachic hour, the Berachot may be recited until the end of the fourth Halachic hour. One who does not recite the Berachot before that time should not recite them that day.
