If you think that God sent Jesus in order to die to satisfy God's own law (aka penal substitutionary atonement – PSA) then it might very well be. Here is Romans 3:21-26 which is often cited as a crucial passage to argue for the centrality of this answer for why Jesus had to die:
But now, irrespective of law, the righteousness of God has been disclosed, and is attested by the law and the prophets, the righteousness of God through faith in Jesus Christ* for all who believe. For there is no distinction, since all have sinned and fall short of the glory of God; they are now justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a sacrifice of atonement by his blood, effective through faith. He did this to show his righteousness, because in his divine forbearance he had passed over the sins previously committed; it was to prove at the present time that he himself is righteous and that he justifies the one who has faith in Jesus.
To be fair, most readings of this piece in Romans argue that it is the center-point of not only Paul's letter to the Romans, but perhaps in his entire theology so it cannot be ignored. I bolded the phrase in question which is a translation of the Greek term hilasterion. Why is this important to note? If this notion of a sacrifice of atonement or appeasement is so central to penal substitutionary atonement, then it seems quite likely that any alternative understanding of the term would destabilize that notion.
Indeed, the footnote to the term in the NRSV translation notes an alternative translation as "place of atonement." Now how is it that Jesus could be a place of atonement rather than the objectof atonment? In other usage, the term Paul uses refers to a gift that someone might place before a god in order to appease that god for something. It could be an fruit, spices, etc. Giving something to a god in order to appease that god's wrath is in keeping with a host of religions including many of those that were popular in the various places Paul travelled.
The problem with understanding this term as used with respect to the atonement is that of agency. In all other uses, it is the human giving the gift to appease God or the gods. But in this case it is God giving God's own self the gift of appeasement or atonement. Strange. Why does God have to give God's own self a gift to appease God's own law? Rather than go with a simple answer that the interpretation of the term could be wrong, PSA proponents need to construct an array of logical propositions to make this idea work. However, as Daniel P. Bailey argues:
By contrast, a more specialized allusion to the biblical "mercy seat" (which is not a gift to the gods) does fit Paul's context, with plenty of support from lexicography (cf. LXX Pentateuch). Paul focuses on "the law and the prophets" and more particularly on the Song of Moses in Exodus 15. The combination of God's righteousness and redemption in Exod 15:13 ("hodegesas te dikaiosune sou ton laon sou touton, hon elutroso") closely parallels Rom 3:24 (dikaioo and apolutrosis). Furthermore, Exod 15:17 promises that the exodus would lead to a new, ideal sanctuary established by God himself. God's open setting out of Jesus as the new hilasterion — the centre of the sanctuary and focus of both the revelation of God (Exod 25:22; Lev 16:2; Num 7:89) and atonement for sin (Leviticus 16) — fulfils this tradition.
As H. R. Niebuhr wrote at the beginning of Chapter IV in The Meaning of Revelation, "When we speak of revelation we mean that something has happened to us in our history which conditions all our thinking and that through this happening we are enabled to apprehend what we are, what we are suffering and doing and what our potentialities are. What is otherwise arbitrary and dumb fact becomes related, intelligible and eloquent fact through the revelatory event." For Niebuhr the event of revelation that makes all other events in human history intelligible is the event of the cross.
The theological impact of the cross is not that God had to give God's own self a gift in order not to provoke God's wrath on humankind. The impact is that God revealed a new Kingdom for which even death was not an obstacle. The cross became the new mercy seat, the new place of the covenant. Jesus as the focus of God's revelation further makes the tearing of the Temple curtain more clear, even if this is a symbolic gesture and not a literal event from the perspective of the Gospel writers. Regardless, the purpose of the cross is in its function as the center of God's revelation.
That God is dead on the cross by Jesus' self-emptying bears a much stronger impact on the role of human agency towards God's revelation. Humans reject God's kingdom and reject this new mercy seat through an act of execution. This is why I argue that it is sin that kills Jesus and not as an act of God to fulfill a law. That a place of execution is a place of mercy is what is shocking and disturbing. The center of the Gospel is not the fulfillment of God's law to repay sin with death. The center of the Gospel is that though humanity will reject God even to the point of execution, God will embrace humanity using love as the means to reveal sovereignty over everything.
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My conclusions on this passage was that hilasterion means "gift given to try to achieve reconciliation", and that in Rom 3 Paul is speaking of God sending Jesus as a gift to humans.
PSA has confused us by teaching us to think of Jesus as targeted at God and appeasing God. However in Paul's view it is humans who need changing not God, they are the ones who hate and oppose God, and it it always them who need reconciling to God not God to them. God thus sends Jesus to Israel, just like he send the OT prophets… to lead them back to God.
I can't agree that a translation of "mercy seat" makes any sense… I can't agree with Bailey that calling Jesus a mercy seat is meaningful. The lexical and contextual arguments all seem to me to point to "reconciliation gift" as the meaning. Paul is clear that the this gift has been given to humanity by God. PSA simply misreads the passage as a gift God gives to God for the sake of humanity.
i can buy gift to achieve reconciliation in this sense as well. but i buy it in the sense that Jesus reveals the gift of the Kingdom of God to humanity and the resurrection ratifies that gift in spite of human hatred towards God. in this sense the mercy seat is indeed a gift, but not in what i think is the irrational sense of what PSA asserts.
i can buy gift to achieve reconciliation in this sense as well. but i buy it in the sense that Jesus reveals the gift of the Kingdom of God to humanity and the resurrection ratifies that gift in spite of human hatred towards God. in this sense the mercy seat is indeed a gift, but not in what i think is the irrational sense of what PSA asserts.
This is the way Paul constructs salvation. "It is NOT those who hear the law who are righteous in God's sight, but it is those who OBEY the law who will be declared righteous." Rom. 2:13
The reason he constructs salvation like this is because after Jesus was crucified a change was made to the law. Actually you are correct that salvation does hang on only a word, but it is necessary to be taught the Way this word must be obeyed to saved.