What "murmur" does patience prevent Milton from making in "On His Blindness"?

The "murmur" is one which Milton, as the speaker, never actually voices—he describes it as the "true account" (which he often feels compelled to present to God) of how he feels, now that his talents have been suppressed by his physical infirmity: his blindness. The choice of the word "murmur" is indicative: a "murmur" suggests something spoken low, as if one is ashamed to say it. The speaker is ashamed that he is not doing as much as he used to in order to serve and please his God; he is afraid that God will come to him and ask him why he is so idle, no longer using his talents to praise his Creator.

In this poem, however, the speaker attempts to console himself and quell the urge to voice such feelings. Instead, he says, God is also served by those who, like the speaker, "stand and wait." It is not always necessary for everybody to be serving God in the same way, as if they were laborers and God their foreman.

In the poem "On His Blindness," "that mumur" refers to Milton's complaint that he cannot serve God because he is blind and his "light is spent," meaning that his sight is used up. His talent is useless because he can no longer see, and he wonders if God still wants him to work, since he can not see. He still is intent on serving God through his talents. Patience stops his murmur, or his complaint that he can no longer work; in other words, if he considers the question patiently, he realizes that God does not require people to work. God only requires that people serve God by waiting or being patient. This is the response to Milton's question--he does not need to serve God by working, but rather by being patient and serving God. 

Why does John Milton refer to his complaint as a "murmur" in "On His Blindness"?

"On His Blindness" is an autobiographical poem that Milton wrote about losing his sight at a relatively young age. Writing much of his poetry about religion and Christian theology, Milton felt that he was in the service of God. He is frustrated by losing his sight as anyone would be. He is particularly frustrated because he has lost his sight while working in the service of God.

When he discusses losing "light," he refers to the loss of his sight and the potential loss of his talent (his intellect and writing). Referring to a Biblical passage, Matthew 25:14-30, the speaker of this poem notes that it is a sin not to use your God-given ability, "that one talent which is death to hide" (3). 

The speaker goes back and forth, from despair to resilience. In lines 1-3, he considers how his light is "spent" meaning used, gone, extinguished. Again, "light" refers to sight and talent. But halfway through line 4, the speaker expresses his resolve to keep serving God. At line 7, the speaker expresses frustration, asking if God expects him to perform a day job (one which is more easily done with light) in darkness. 

"Doth God exact day-labour, light-denied?"
I fondly ask.  But Patience, to prevent 
That murmur, soon replies: "God doth not need
Either man's work or his own gifts: who best 
Bear his mild yoke, they serve him best. (7-11) 

The speaker's frustration is immediately mitigated by his thought that he should be patient and accept this burden (yoke). He uses the word "murmur" because he is conflicted about whether to despair or persevere. Had he been completely frustrated, his murmur would have been a shout. Had he been completely resilient, he would never have murmured or shouted any complaint. A murmur is like a half-hearted complaint. He is frustrated but resilient. Therefore, his complaint comes out quietly and humbly.