The Gemara of Berachot concludes that the halachah 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 therefore 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 – from this point on, he has not forfeited [the berachot.]”
The Rambam (a”h) and the Rif (a”h) held that one may recite the berachot the entire day, until sundown. The Ritva (a”h) and some of the Tosafot held that one may recite the berachot only until chatzot (midday), whereas the Rosh (a”h) ruled even more stringently, claiming that the berchot must be recited by the end of the fourth halachic hour.
The Shulchan Aruch follows the stringent view of the Rosh, and allows one to recite the berachot of Shema only until the end of the fourth hour. However, with regard to the berachot, one may rely on the later of the two calculations of the final time for Shema. With regard to the recitation of the Shema, one should endeavor to follow the stringent view, and recite Shema before the earlier of the two times.