In the poem "To His Coy Mistress," what is the speaker's basic argument?

The basic argument of this poem is that if time were limitless, the woman's coyness would not matter. She keeps putting off the narrator of the poem, but the narrator argues that her coyness is wasting time, as time is finite.
The poet says that if time were limitless and they were immortal, they could walk, even to the Ganges in India, and he could spend centuries admiring her beauty. She could also continue to refuse him to the "conversion of the Jews" (which means forever). However, as they are not immortal, if she keeps putting him off, she will die before they can get together as a couple. All her coyness will be for naught, as they will never get to enjoy their love. They should instead find love when they are young and can enjoy it. In simple terms, the message of the poem is "carpe diem," or seize the day.

Andrew Marvell's "To His Coy Mistress" is an especially famous example of seventeenth-century "carpe diem" poetry. Like other works in the genre, Marvell's poem centers on the fleeting nature of life and youth and the consequent need to make the most of them while they last. In this particular poem, the speaker is leveraging this argument to persuade his "coy" (shy or hesitating) lover to sleep with him. He begins by acknowledging that the woman "deserves" a long and extravagant courtship, and he speaks hyperbolically about devoting hundreds of years to praising each of her body parts (19). At this point, however, the speaker switches strategies and reminds his lover that time is constantly passing ("at my back I always hear / Time's wingèd chariot hurrying near") and that death is inevitable; in the end, the woman will lose her beauty, and "worms" will take her "virginity" (21–22, 27, 28). That being the case, the speaker says, there is no time to waste on slow, leisurely lovemaking. Instead, he uses urgent and even violent language ("tear our pleasures with rough strife") to convince his mistress to accept his advances; by snatching what pleasure they can from the moment, the couple can defy (if not stop) the progression of time ("though we cannot make our sun / Stand still, yet we will make him run" (43, 45–46).