The legal basis for the suggestion that the decision does not take effect immediately is Supreme Court
Rule 45(2), which provides that the formal mandate will not generally issue until 25 days after the decision, unless the parties agree otherwise. Rule 45(3) says that when reviewing an order of a federal court, no formal mandate will actually issue, but that Rule 45(2) otherwise applies. The exact meaning of these rules is pretty unclear in this context.
The "mandate" of a Court is a name for its formal order, directing the parties on exactly what to do in response to the decision. In Canada, the term "reasons for judgment" is sometimes used for the opinion, while the mandate itself is strictly called the "judgment". However, those terms are a bit misleading because the general rule is that (in the absence of a rule of court that says otherwise), the reasons for judgment are self-executing even if never memorialised into a formal mandate. Although that's already the default rule, some courts choose to affirm it explicitly in their rules. For example,
Rule 9.6 of the Alberta Rules of Court says that the judgment of the Court comes into effect on the date of pronouncement, whether or not the mandate has been formally issued. Rule 45 of the US Supreme Court apparently takes a different approach, but the exact legal effect here is unclear.
As mentioned, there will not be any physical mandate in this case because it was a federal case and Rule 45(3) dispenses with formal mandates in such cases. However, if there
were a formal mandate, it would not say anything like "every state must now licence marriages without regard to sex", because that's merely the
reasoning behind the judgment; it's not the judgment itself. The mandate, if one existed, would be limited solely to: "The judgment of the Sixth Circuit Court of Appeals is hereby reversed." That is the only order whose issuance Rule 45(2) is arguably delaying by 25 days.
But what is the legal effect of reversing the judgment of the Sixth Circuit? To understand that, we have to take a step back and understand what the mandate of
that Court would have been. The procedural history of the case is that the plaintiffs filed suit in various district courts to obtain recognition of their own marriages. The district courts ruled in favour of plaintiffs and issued various injunctions to compel such recognition. On appeal, the Sixth Circuit reversed those effects, and the sole provision of its mandate in each case would be something to the effect of: "The judgment of the district court is reversed, and the injunctions are vacated." When the theoretical Supreme Court mandate issues in 25 days, the order of the Sixth Circuit will be reversed, which means that those injunctions will be restored, and the officials in the specific states involved in the case will be compelled by court order to give recognition to marriages according to the terms of the injunction. However, that only applies to the states actually involved in the case (not every case in the country), and generally only according to the terms of the injunctions which may not include every couple in the state.
However, now that the Supreme Court has declared of the land, there is no rule that requires a state official to wait to be enjoined to act in accordance with the law. In other words, states are free to comply with the law as declared herein even if no injunction compels them to do so. The law takes effect immediately; the only thing delayed is the injunctions to specific state officials in the states actually party to the case.
Some states in the US were not parties to the case. For those states, nothing interesting will occur in 25 days. The state officials will instead decide (at any time) whether to follow the law or not. If they decide to follow it, they need not wait for the formal mandate of the Court, which has no direct relevance to their state; instead, they can follow it at any time. If they decline to follow it, affected couples will need to separately seek injunctions in courts in their own states; the mandate of the Supreme Court in this case will not have that effect by itself.
As I mentioned, the text and effect of Rule 45 is far from clear, especially as it applies to federal court review. As a result, it has been sometimes interpreted as not even delaying the effective date of the reversal of the court of appeals. For example, consider the case of
Hollingsworth v. Perry, popularly known as the proposition 8 case. The district court judge in that case ordered state officials to comply with certain injunctions. That order was stayed pending review. The reasons for judgment of the Supreme Court, affirming the decision of the district judge, were released on June 26, 2013. A mere two days later on June 28, 2013, the Ninth Circuit dissolved the stay and brought the district court's injunctions into effect immediately:
Perry v. Hollingworth (
Doc #432). The supporters of proposition 8 filed papers in the Supreme Court asking it reverse the Ninth Circuit on the basis that since no hypothetical mandate had yet issued, the Ninth Circuit lacked authority to vacate the stay, but Kennedy J denied that motion without reasons on June 30, 2013.
In conclusion, the effect of Rule 45 is unclear.