I hesitate at your qualifier "modern," but otherwise I would answer with a resounding, "YES!" An emphasis on "revival" or awakening or zeal for God, soul-winning spirit, Holy Spirit filling, or repentance from sin is definitely needed, and certainly demonstrated in the New Testament.
But all that is called "revival" is not necessarily what is true revival. Using fleshly methods never has produced spiritual results, and never will. They that truly worship the Living God, Who is a spirit, must worship Him in spirit and in truth.
New Testament support? 5 of the 7 churches in Revelation are good for starters. Especially is this true of Sardis, the dead church. Christ's multiple admonitions to these churches to "repent" and do things differently, to walk as they did once before, and especially to "strengthen the things which remain, which are ready to die," (Rev 3:2) demonstrate that Christ, the Lord of the Church, places heavy emphasis on reviving.
Corinthians does rebuke some things, a whole host of them. But in ending his first letter to them, the Apostle attempts to jar them awake!
1Co 15:34 Awake to righteousness, and sin not; for some have not the knowledge of God: I speak this to your shame.
In chapter 5, they had been arrogant and prideful of their tolerance to sin in their midst. Now Paul emphasizes what should be their shame. They are in need of revival! And as a result of that emphasis, we see in 2Corinthians 6 that they got one.
2Cor 6:8-13
8 For though I made you sorry with a letter, I do not repent, though I did repent: for I perceive that the same epistle hath made you sorry, though it were but for a season.
9 Now I rejoice, not that ye were made sorry, but that ye sorrowed to repentance: for ye were made sorry after a godly manner, that ye might receive damage by us in nothing.
10 For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death.
11 For behold this selfsame thing, that ye sorrowed after a godly sort,
what carefulness it wrought in you,
yea, what clearing of yourselves,
yea, what indignation,
yea, what fear,
yea, what vehement desire,
yea, what zeal,
yea, what revenge!
In all things ye have approved yourselves to be clear in this matter.
12 ¶ Wherefore, though I wrote unto you, I did it not for his cause that had done the wrong, nor for his cause that suffered wrong, but that our care for you in the sight of God might appear unto you.
13 Therefore we were comforted in your comfort: yea, and exceedingly the more joyed we for the joy of Titus, because his spirit was refreshed by you all.
These are very clearly revival RESULTS lived out in the Corinthian believers! Paul emphasized an error, and they sorrowed, repented, and acted to clear themselves with zeal.
Should we emphasize revival? Are we content, then, with what we currently have? Afraid of moving from crisis to crisis? In Corinth, there was a crisis of fornication within the church and that treated as a badge of honor! The entire first epistle to Corinth was "moving from crisis to crisis." We need to deal with issues instead of settling back on our lees and hoping for people to do better. Today, there is a crisis of wickedness in the pulpits, the classrooms, and churches of all denominations, stripes, and sizes. Are we complacent? Or will we recognize that we NEED a refreshing and emphasize it? Shall we just continue to sin that grace may abound? Are we happy while the basic structure of the family is destroyed and perversion springs from every closet? While the defenseless are destroyed in the womb? Are we to be comfortable while liquor, recreational drugs, lewdness, debauchery, and violence explodes all around us?
In John 4, the 12 disciples left Christ alone and went to feed their bellies. His meat, His need was to deal with a sinful woman coming to draw water at a well. No, the LORD did not hang out a "REVIVAL" banner or promote "At The Well the Next 3 Nights, 7 pm Nightly," but when He met resistance from the woman who first threw her racial differences at him, then her different religious background, He addressed her sinful condition and spoke of spiritual matters, instead of acting with apathy and dispassionate tolerance. As a result, 12 men went to a city and brought back sack lunches; one redeemed woman went to that same city and turned out men for a revival. Now, which do we want to be today?
Because some perform in error, do we resign ourselves from what is right? When men promote "soul-winning" with an easy-prayerism methodology like a vacuum cleaner saleman, should we then toss out the Great Commission as something that cannot be done? No, instead we do what is right. If liberals use liberty as an occasion to the flesh, should we ride that pendulum the full arc to legalistic bondage? No, it is better to do right rightly in the face of those who do right wrongly rather than not doing right at all.
To the Ephesian church, Paul emphasized revival.
Eph 5:14 Wherefore he saith, Awake thou that sleepest, and arise from the dead, and Christ shall give thee light.
We need to wake up lethargic churches! Not by method, not by rote, but certainly by shining forth the bright light of Christ.
Paul would remind Timothy as an individual to "stir up the gift of God." (2 Tim 1:6) Peter in his first epistle thought it was the right thing while he was still living to "stir up" fellow believers (2Pet 1:13). Today, too often, believers are merely "shaken, not stirred."
Hebrews 11 reveals that faith is a dynamic. Flawed men were applauded by God, not for their errors which do not please Him, but for their faith which did please Him and which also "subdued kingdoms, wrought righeousness, obtained promises..." etc. Sure sounds like the kind of revival I would like to see. Not the mere motions of going through another meeting, but the honesty of seeking the LORD in the prayer closet and proclaiming His truth with power, so that those promises of power He has given are appropriated through faith. It was not mere mechanism that such as Leonard Ravenhill would promote, but real prayer and getting hold of God. btw... There is a God, and yes, He does still answer prayer, He does still work miracles, and He does still send revival in answer to the heart cries of men like those who may have been Old Testament saints, but were still mere mortal men "of like passions" as we are today.
Finney may have been mistaken in some ways, but he was used of God. I would gladly trade three John MacArthur's and toss in an extra Phil Johnson or two for a Charles Finney, today ... or that great Revivalist Charles Spurgeon, or perhaps a preaching fireball like John Wesley, certainly a Jonathan Edwards, or a Nate Saint, or a D.L. Moody, or a Billy Sunday, or a Christmas Evans, or an Reuben Archer Torrey, or give me another in the spirit of Whitfield, or perhaps Hudson Taylor, or Sam Jones, or B.R. Lakin, or Vance Havner or an A.W. Tozer. We may not need to be overzealous, but we certainly need some zeal.
You may see dangers in emphasizing revival, but there is greater danger in ignoring its need. The smug, self-serving complacent attitudes of today rob our churches of fiery zeal and motivating power turning them into vast wastelands of dry, stale, abandoned ghost towns. The LORD Jesus Christ Himself did not merely let the coming power of the Holy Ghost happen on Pentecost, but repeatedly gave His disciples instruction to wait for that promise, and told them of the blessings that the Comforter would bring. Yes, my friend, we do much need to do the same and emphasize it where we can. We may have everlasting life, but we need more abundant life. Peter said we were lively stones. I prefer to emphasize the lively; some, I fear, prefer to emulate mere stones.