Q. I wonder constantly why do we say every day three times a day in the amida in the bracha dedicated to the coming of Mashiach, the words “ki lishuat’cha kivinu kol hayom,” or “since we hope for Your salvation the whole day, and wait” Is that not lying openly to Hashem? How could we be so brazen?

A. Horav Shlomo Miller Shlit”a explained that there are different degrees of consciousness in the mind. At some subliminal level all Jewish souls posses a constant desire for salvation and Bias Hamoshiach.
The Radal (Hagohos on Shir Hashirim Rabbo ch. 7) maintains the correct girsa or wording is Kol Yom, (every day) omitting the letter ה, because of that same concern. However, Talelei Oros (Tefilos p.320) quotes that the Brisker Rov zt”l would interpret the Tefila literally as it is written. The above (ibid.) also quotes Horav Yosef Shoul Natanzon zt’l as explaining that the day in this tefila, refers to the day of Hashem, which is a thousand years.
Other interpretations aver that the tefilos are said in plural since they include the whole nation of Israel. Indeed, when we consider everyone together the statement is true (Rabbi S. Spero). In addition, the word “kivinu” is past tense. Certainly, in the past there were great tzadikim, that could have sincerely said that statement. (R’ Avner Milevsky.)
The word “Ki” also has different meanings, adding to “since” the words “if”, “maybe” and “but.” Some of those interpretations may provide an answer.
Horav Yaakov Galinski zt’l (Vehigadto Balak) explains that everyone expects and desires a yeshua, salvation or help, since that is the normal human condition. What exactly that yeshua entitles depends on the individual. For some it may be something quite banal and inconsequential; for others it is indeed the real thing.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a