"We shall receive the most fierce opposition from the Adventists who oppose the law of God. But, like the builders of the walls of Jerusalem, we should not be diverted and hindered from our work by reports, by messengers desiring discussion or controversy, or by intimidating threats, the publication of falsehoods, or any of the devices that Satan may instigate. Our answer should be: We are engaged in a great work, and we cannot come down. We shall sometimes be perplexed to know what course we should pursue to preserve the honor of the cause of God and to vindicate His truth. 3T 574.2"
"And I sent messengers unto them, saying, I am doing a great work, so that I cannot come down: why should the work cease, whilst I leave it, and come down to you?"
EGW directly quotes and applies Nehemiah's statement about being too busy with important work to be distracted, making a clear connection.
"The course of Nehemiah should have a strong bearing upon our minds as to the manner of meeting this kind of opponents. We should take all these things to the Lord in prayer, as Nehemiah made his supplication to God, while his own spirit was humbled. He clung to God with unwavering faith. This is the course that we should pursue. Time is too precious to be devoted by the servants of God to vindicating their character, blackened by those who hate the Sabbath of the Lord. We should move forward with unwavering confidence, believing that God will give His truth great and precious victories. In humility, meekness, and purity of life, relying upon Jesus, we should carry a convincing power with us that we have the truth. 3T 574.3"
"Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God."
While not a direct quote, the EGW passage shares the theme of taking concerns to God in prayer, similar to Philippians 4:6. However, the connection is not as strong as a direct allusion.
"We do not understand, as is our privilege, the faith and confidence that we may have in God, and the great blessings which faith will give us. An important work is before us. We are to obtain a moral fitness for heaven. Our words and our example are to tell upon the world. Angels of God are actively engaged in ministering to the children of God. Precious promises are upon record on condition of our obedience to God's requirements. Heaven is full of the richest of blessings, all waiting to be communicated to us. If we feel our need, and come to God in sincerity and in earnest faith, we shall be brought into close connection with heaven and shall be channels of light to the world. 3T 574.4"
"Whereby are given unto us exceeding great and precious promises: that by these ye might be partakers of the divine nature, having escaped the corruption that is in the world through lust."
Both passages discuss precious promises and their connection to obedience and blessings. The link is thematic, not a direct quote or explicit reference.