Arminians and other varieties of non-Calvinists reconcile the all-powerful nature of God with His allowance of free will to men, within the limits of physics he has given them, as God constrains Himself to His own purpose and character. In so keeping, it is God's character and not His power that is the 'limiting factor' in why, though it is His desire that all men be drawn to Christ (Jn 12:32) and that all men might be reconciled to Him through Christ and believe (Jn 1:7), He made the only way to Salvation the free choice of placing one's faith in Christ and not some other method of universal salvation (John 14:6.)
This, in many ways, is like unto a sovereign king who does not remove the will of his subjects or force their every action into compliance. Rather, he sets up boundaries/limits in which people can act. If they disobey, they are punished. The king does not even force the actions of his military or servants. Rather, the soldiers and servants have even stricter discipline and rules binding them than the civilians. If they disobey, they are court-martialled or punished. If they obey and do good service, they are promoted or rewarded. The king also delegates authority; his authority even over his highest ministers to guide, punish, and reward is a mark of his sovereign power.
As such, there is no contradiction between an all-sovereign King who is technically powerful enough to force his way in all regards, and a people that are capable of free volition.
As summarized in an extensive article by Jack Cortell explaining how the Arminian view of man's free will does not limit the power and sovereignty of God, "We have affirmed that the will of man is free, and that this very freedom is a part of God's all-inclusive, sovereign decree"
http://www.dabar.org/SemReview/sovfrwill.html
Scripture shows in detail how God's supreme sovereignty and power plays out, and how in many cases He simply sets limits or boundaries according to His will rather than continually micro-managing the cosmos or people.
He puts boundaries and limits on nature. (Jer 5:22, Job 38:4-41, Job 9:4-9, Psalm 104:1-13, Lev 26:3-5, II Chron 7:11-16, Jer 8:7, Jer 10:13)
He puts boundaries and limits on the life and history of man and the nations (Job 14:5, Acts 17:26, Num 34:1-12, II Chron 13:4-18, I Kings 9:5, Psalm 2:1-12, Jer 45:4, Luke 12:25, II Kings 7:1-20, Gen 22:8-14, Isaiah 45:9-13, Dan 4:34, Dan 2:21)
He makes provision for nature and man (I Chron 29:12-15, James 1:17, Psalm 84:3, Psalm 104:14-23, Psalm 104:27-30, Psalm 12:5, Matt 6:26)
He tasks us as His servants to perform His will (Acts 1:8, Rom 12:2, II Cor 10:13-15, Matt 14:13, I Thess 5:12-18, I Pet 2:15, Heb 10:36, I Cor 4:1, Rom 2:13)
He gives us power to perform His will (Ex 10:1-20, Rev 11:6, Acts 1:8, Heb 11; Phil 2:12-13, Ezra 6:1-12, I Peter 4:10, Mark 16:15-18, Isaiah 45:1-7)
He sets the standard of righteousness (Rom 1:17, Psalm 18:30, Eph 2:3, Psalm 119:3, Deut 32:4, PSalm 145:17, Isaiah 5:16, Isaiah 51:6, Dan 9:14, Jer 9:24)
He punishes the wicked and is the final judge of the fate of man (I Pet 3:10-12, Rev 20:11-15, Isaiah 13:11, Rom 6:23, Psalm 145:20, Rom 2:6-10, II Thess 2:8)
He sets the rules by which deliverance, forgiveness, and pardon are obtained (Num 25:22-29, Jer 26:1-6, II Chron 7:14, John 3:16, Heb 10:11-18, Luke 4:14-21, Heb 9:22, Matt 5:29, Isiah 45:22-25)
He makes righteous laws and decrees (Ex 19:12-23, Lev 20:8, Psalm 93:5, Num 23:19, Deut 6:1, Rom 1:32, Rom 5:18, Rom 10:4)
He appoints others to carry out His decrees [God delegates] (Heb 1:14, Matt 25:14-30, Hab 1:6, Zech 11:16, Amons 6:4, Acts 3:26, Gal 4:6, John 3:31-36, II Chron 18:21, I Kings 14:14, I John 4:10)
He punishes the servants that do not follow his decrees (Matt 25:24-30, II Pet 2:4-22, Mal 3:17-18, Matt 18:21-35, )
He binds even time and space to subject to His eternal plan (Heb 4:7, Rom 16:25-27, Rom 8:22-25, Rev 21:21, II Pet 3:3-10, I Cor 2:7, I Pet 1:20, Isaiah 46:9-10, Acts 2:23)
His kingdom is eternal and cannot be destroyed by man or Satan (Dan 7:13-27, Eph 1:15-23, I Chron 29:10-13, Rev 1:18, II Pet 1:10-11, Psalm 145:13, Dan 6:26, Dan 2:44, Matt 6:19-20)
Arminian scholar Roger Olson summarizes how God's own character and sovereign plan limit God's own actions or control in this way,
“CLASSICAL Arminianism goes far beyond belief in general providence to
include affirmation of God’s intimate and direct involvement in every
event of nature and history. The only thing the Arminian view of
God’s sovereignty necessarily excludes is God’s authorship of sin and
evil. Faithful followers of Arminius have always believed that God
governs the entire universe and all of history. Nothing at all can
happen without God’s permission, and many things are specifically and
directly controlled and caused by God. Even sin and evil do not
escape God’s providential governance in classical Arminian theology.
God permits and limits them without willing or causing them.”
A fine example of authority and willful obedience working together is from Matt 8:5-18.
A centurion approaches Jesus and asks Him to come heal his servant. Jesus asks "shall I (personally) come heal him"? The centurion says no, but asks for "Jesus' word" instead. The centurion is a man under authority (the king, higher officers) but is also over other soldiers. He tells them "Go", and they go. They do not go because they are forced by the centurion, but because they having willingly submitted themselves to the authority of the centurion. As such, the centurion has faith that if Jesus merely commands it, then it will be done (and it is!).
In short: The two aspects (God's ultimate power, and God giving the choice to man whether to place faith in Christ) are not seen by Arminians and many other non-Calvinists as being at odds, as the ability for man to act in obedience under God's commands, or rebel and disobey and God's authority to punish, is actually a mark of God's supreme sovereign power and not a detraction from it. Believing that man has a free will to act and choose obedience is not viewed as contradicting or minimizing God's power and kingship - quite the opposite, it is viewed as enhancing it.
