I imagine a new constitution rewritten by todays officials would start something like this:
"We the federal government, in order to maintain a stable Union, establish precedence, protect domestic security, provide for the common defense, promote the general health and welfare, and recognize the concept of Liberty within reason to ourselves and our posterity, do establish this Constitution for the United States of America."
Article I would establish the veto power of the president over the legislature, with language establishing the legislature's ability to suggest laws as needed.
Article II would firmly describe the executive branch's role in establishing and maintaining security by all means required, as established by the will of the President. It would also describe the election cycle, with a series of triggers that would activate a term-extension "in times of national distress". This would be colloquially known as the "don't change horses midstream" clause.
Article III would create the Law & Order department, which starts with a Supreme Court like today, establishes the existing court structure we have, and explicitly provides for situations where defendants can be removed from the legal system and tried or judged separately without the constraints our current system have "in the interest of tranquility".
Article IV would clearly establish that the states have an advisory role in setting the direction of funding and internal rule, but that all of their laws would be replaced by a standardized federal legal structure. The funding and running of the courts would, of course, be done locally, but by all appointed federal personnel.
Article V would, like the current constitution, establish the amendment procedure, but with some important differences. An executive veto would be added, as would the means for temporarily suspending parts of the constitution as needed by the determination of the executive branch.
Article VI would re-iterate the federal nature of all national laws, plus allow for special dispensation for churches to be federally funded to establish local arms of the government. The efficiency of simply appointing local priests and such as federal officers to ensure domestic tranquility would be very attractive, as they would already have the public trust.
No need for Article VII, ratification would be taken care of by the appropriate congress, the executive branch would then inherit the above described abilities.
We'd also have a new section:
The bill of privileges
1. Except for obscenity, all speech is free. Obscenity is defined as opinion text or speech that causes discomfort or the potential for discomfort to its readers.
2. Hunting rifles are, under certain circumstances, allowed with the appropriate federal oversight.
3. The military shall not quarter soldiers in your house unless it is deemed necessary.
4. Reasonable searches by local and federal law enforcement are allowed, the boundaries to be defined as needed nationally.
5. In the pursuit of justice and the common good, criminals and uncooperative property owners shall be dealt with quickly and justly.
6. A speedy trial is guaranteed and encouraged, except when doing so would go against the common good.
7. When feasible, a trial by jury shall be allowed, though the jury will preside in an advisory role.
8. In the interests of national defense and tranquility, special means may be authorized in confining or interrogating enemies of the peace.
9. This list of privileges may be suspended or canceled as needed in the interests of national tranquility and security.
10. Finally, this reiterates Article IV of the New Constitution, specifically that the states exist as internal advisory bodies only.