Is there will power & endurance required in order to renounce worldy pleasures? I am particularly speaking of those people who did not experience (profound) meditative bliss à la sukha or various jhanic states yet.
In Pali Canon, Buddha gives the following image of Will Power:
Gladly would I let the flesh & blood in my body dry up, leaving just the skin, tendons, & bones, but if I have not attained what can be reached through human firmness, human persistence, human striving, there will be no relaxing my persistence.
According to my teacher, if you look at Will Power closely, you will see that it's actually made out of multiple distinct factors:
Inspiration - first, we're inspired by an example of the teacher or the beauty of a tradition.
Objective - because we're inspired by an image of happiness, freedom, perfection etc., we want to attain it, we want to be like the Buddha or like our teacher.
Commitment - then we make a firm decision. In case of renouncing worldly pleasures it's a firm decision to not enage in worldly pleasures. In case of abandoning negative thinking, it's a firm decision to not cultivate the negative thinking. In case of cultivation of suchness, it's a firm decision to not think that you lack any further achievements etc.
Cultivation - now that we have made the decision, we must stick to it despite all sorts of obstacles and distractions, including the ones that disrupt our Commitment by distracting us into other frames of reference in which the original Objective does not make sense. So we repeatedly engage our attention with stimuli that help sustain and generate the right kind of Inspiration and we avoid the stimuli that mess with our Commitment.
Forbearance - as we do the above, we keep running into situations that result in psychological pain because of the conflict between our commitment and the distracting stimuli pulling us in other directions. This type of pain is inevitable side-effect of practice and we must learn to endure it.
Taken together, these factors constitute Will Power. It is important to understand the exact mechanics of how the will power works, rather than naively assuming we can achieve success by applying brute force.
The first two factors happen automatically, without our control. We get inspired by an idea and we want to be like that, too. The other three factors depend on us. We must make a firm determination or commitment to stick to a specific frame of reference. We must guard our minds from distractions and demotivators. We must seek inspiration again and again, by turning our attention to and going over the inspiring ideas, in order to keep our motivation high. We must be prepared to face the conflict-generating aspect of commitment and the pain it creates. Without putting effort in these three factors, our original inspiration will die out very fast.
So while Will Power matters, what's important in Buddhism is developing skilful means for working with (mental) causes and their effects.
It is sometimes said that the way of the Saint is will-power and the way of the Sage is knowledge. The Saint needs will-power and battles day and night against worldly-pleasures to forcibly kill them off. The Sage allows his or her practice to do its work at its own pace and generally has an easier time of it. But then, it might be argued that will-power is required to keep up the practice.
I feel that will-power is a profound topic and am not sure there is such a thing. This is suggested by the answer given by Andrei above. I seem to remember Sri Ramana Maharshi stating that the 'will of God' is a muddled idea (why would God need a Will?), and suspect most ideas of 'will' are muddled. They assume an agent who willfully acts while the existence of such an agent is denied by the Perennial philosophy.
Just thinking out loud.
Will power & endurance is ardent, persistence factor for Awakening, and right effort to putting aside greed & distress with reference to the world according to DN Mahāsatipaṭṭhānasutta:
The Blessed One said this: "This is the direct path for the purification of beings, for the overcoming of sorrow & lamentation, for the disappearance of pain & distress, for the attainment of the right method, & for the realization of Unbinding — in other words, the four frames of reference. Which four?
"There is the case where a monk remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world. He remains focused on feelings... mind... origins in & of themselves — ardent, alert, & mindful — putting aside greed & distress with reference to the world.
There is the case where, there being persistence as a factor for Awakening present within, he discerns that 'Persistence as a factor for Awakening is present within me.' Or, there being no persistence as a factor for Awakening present within, he discerns that 'Persistence as a factor for Awakening is not present within me.' He discerns how there is the arising of unarisen persistence as a factor for Awakening. And he discerns how there is the culmination of the development of persistence as a factor for Awakening once it has arisen.
[d] "And what is the noble truth of the path of practice leading to the cessation of stress? Just this very noble eightfold path: right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration.
"And what is right effort? There is the case where a monk generates desire, endeavors, arouses persistence, upholds & exerts his intent for the sake of the non-arising of evil, unskillful qualities that have not yet arisen... for the sake of the abandoning of evil, unskillful qualities that have arisen... for the sake of the arising of skillful qualities that have not yet arisen... (and) for the maintenance, non-confusion, increase, plenitude, development, & culmination of skillful qualities that have arisen: This is called right effort.
"And what is right mindfulness? There is the case where a monk remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world. He remains focused on feelings in & of themselves... the mind in & of itself... origins in & of themselves — ardent, alert, & mindful — putting aside greed & distress with reference to the world. This is called right mindfulness.
"In this way he remains focused internally on origins in & of themselves, or externally on origins in & of themselves, or both internally & externally on origins in & of themselves. Or he remains focused on the phenomenon of origination with regard to origins, on the phenomenon of passing away with regard to origins, or on the phenomenon of origination & passing away with regard to origins. Or his mindfulness that 'There are origins' is maintained to the extent of knowledge & remembrance. And he remains independent, unsustained by (not clinging to) anything in the world. This is how a monk remains focused on origins in & of themselves with reference to the four noble truths...