First, let's clear away a few possible misconceptions. Heavenly citizenship, and a related 'illegal alien' status, does not come down to race, ethnicity, nationality, or gender. It comes down to humility, repentance, faith, hope, and charity. Second, St. Peter won't be checking our membership card for an (R) or a (D), or even an (I), but will look straight into our heart to see if it burns for Jesus.
So, dispensing with silly temporal politics, let's consider 'the stairway to heaven.'
"Then shall you know that I, the LORD, am your God, dwelling on Zion, my holy mountain; Jerusalem shall be holy, and strangers shall pass through her no more. And then, on that day, the mountains shall drip new wine... A fountain shall issue from the house of the LORD...Egypt shall be a waste...Because of violence done to the people of Judah, because they shed innocent blood in their land. But Judah shall abide forever, and Jerusalem for all generations. I will avenge their blood, and not leave it unpunished. The LORD dwells in Zion." Joel 4:12-21
Heaven is the abode of those who die to self and live 'Thy Will be done.' On record, only one human person has been Perfect enough to fulfill this--the God-man Jesus Christ. Though Mary was sinless, she was sinless through Jesus her Son. Though the saints win victory in virtue over vice, this comes with much struggle, and, once again, it is via Jesus. For us, it is much the same. We can, and must, choose for the good if we want to live heavenly with Goodness Himself. This, however, can only be accomplished in the Life of Christ, especially blessed for Catholics in the Eucharistic Life. That is why heaven harbors no illegal aliens. Only those truly willing to die to self (Cross) and take up the Life of another (Jesus) can enter on truly Holy ground. For Christ's Blood was shed in Mercy so that we could join in His Suffering for true Justice in dying to self for the Love of God.
And this is the mark in our heart which St. Peter seeks upon entrance.
"The mountains melt like wax before the LORD, before the LORD of all the earth. The heavens proclaim his justice, and all peoples see his glory...Light dawns for the just; and gladness, for the upright of heart." Psalm 97:1-2, 5-6, 11-12
The greatest obstacle to heaven is a distorted view of God's majestic creation. When human bodies and human creations and human ideas become greater than the Source of all good things, idolatry runs the land. America is in such peril. Salvation, however, is in climbing the highest mountain, in sailing the largest sea, and pondering the greatest human achievement only to understand them as nothing but melting wax next to the Fire of the Lord's Love. But this can only come when Joe and Jane Proud-Peacock are knocked to their ass and feel the heat of personal depravity and the breeze of gratuitous grace in Divine forgiveness. Then, and only then, may they see a glimpse of wisdom, and feel a pinch of joy, in the holy virtue which comes from God.
“'Blessed is the womb that carried you and the breasts at which you nursed.' He replied, 'Rather, blessed are those who hear the word of God and observe it.'” Luke 11:27-28
This shouldn't be taken as a slight against the Blessed Virgin Mary, Mother of God, Queen of heaven and earth, Advocate of those in 'the valley of tears.' Rather, it should encourage the large horde of sinners like us, who can hear the word of God and observe it...through the Apostolic witness of the Church and the Holy Spirit given us (through the suffering Love of Jesus) in the Mercy of our Prodigal Father in Heaven. In Divine grace, therefore, we, like Mary, can say 'yes' to God.
And this 'yes' is precisely what gets us to heaven...even if we have to dock temporarily in purgatory to have the barnacles scraped off our impetuous soul. But that's another story.