I want to see this attempted. The two seem inherently different from my perspective, since in my understanding, progressives want to enlarge government while libertarians want to shrink it, but let's see. Feel free to post another definition of progressivism.
I'd like to keep the topic going for as long as it doesn't fall into blatant hypocrisy, as these threads so often do.
Progressives, as a rule, hold to Keynesian economics while Libertarians hold to Austrian economics. There's also another branch, called Chicago or Freshwater economics, which takes a sort of middle-ground. While these don't, per se, apply to regulation of business directly, they do tend to take similar levels of positions regarding how much regulation there should be or where. Regardless, any serious progressive understands that there can be bad regulations, and and serious libertarian understands the concept of an externality. You can pick many individual issues, and narrow down on specifics, like "Should the government ensure care for tuberculosis?" and, once people understand all of the factors involved, get the same answer from both libertarians and progressives. Likewise, the same is true for "Should the government structure benefits such that these benefits drop off faster than their income rises?" This last is roundly mocked by both libertarians and progressives alike, and an easy common ground to start from between libertarians and progressives on social welfare.
In general, though, my desire for a New Bill of Rights usually covers things that Libertarians and Progressives will generally agree on:
1) Possession, whether on one's person, in or on one's vehicle, or on one's property should not be considered, alone, as evidence for a crime against such a person. Most such incidents involve non-violent crime that should not be illegal anyway (pot usage), are used to frame people, or hinder the reporting of actual crime (you can be convicted of trafficking in child pornography yourself by reporting child pornography to the police improperly). Anyone convicted solely on these grounds should have their sentences instantly pardoned.
2) It should not be possible for an executive to pardon an individual. Rather, they may pardon crimes, effectively declaring them null and void - another means of declaring a law unconstitutional, but from the Executive rather than Judicial branch. It may, at the federal and optionally at the state levels, require some additional support to 'check' its power, but this would remove pardons from what currently looks like a blatant favor exchange and instead give us another way to remove bad laws.
3) A person should not be subject to prison or detainment, for any length of time, due to debt. 'Debtor's prisons' are already unconstitutional in many states, it should be implemented at the federal level.
4) A clear definition of usury is required, and constitutionally enforced by means of requiring that a debt be considered void and unenforceable if it ever exceeded this value. This is most commonly an issue because of preying on the ignorant through Payday Loans and ARMs, where people get tricked into paying ridiculously high interest rates. Picking a good definition of usury will be difficult, but could be tied to the inflation of a specific basket of goods, plus ~.05% per day (this would amounts to a maximum of 20% APR over the rate of inflation).
5) In order for someone to be legally recognized as having the right to collect on a debt, they must also recognize the right to bankruptcy, save for debts incurred SOLELY because of 1) Willful harm of another or 2) Willful destruction of property. In all other cases, all property would be ceded and auctioned, save for a select amount of property to ensure that they can get back on there feet. At a minimum, they should be allowed to be retain a reasonable means of transportation, reasonable means of communication and savings to pay for such, reasonable means of housing and savings to pay for such, and for self employed and those who own their own tools for their work, retain these to reasonable points. There must be no court or filing costs for individuals declaring bankruptcy - a person wishing to do so notifies the local sheriff, and has their excess goods noted, seized, and auctioned (for most debtors, this will be nothing).
Records of such bankruptcies may be recorded, as public knowledge, indefinitely.
This actually is less for protecting the people who would declare bankruptcy under such a scheme (at least, those who are aware of their current rights). Rather, it helps to force the bad-loan market to do more self policing.
6) There should be no such thing as software patents, business method patents, and their kin, and any and all rulings from Amazon's one-click patent on should be declared unlawful, with the judgments fully rendered void. Similarly, 'product patents' should be declared void as a class, as should patents which claim ownership of natural phenomenon such as the human genome.
7) Copyright should last 40 years, at most. 20 would be better. It may be prudent to recognize moral rights for longer, or even indefinitely - but copyrights do need a relatively quick expiry.
I could go on. Making a clear definition of the freedom of speech, clearly defining a right to privacy, clearly defining a right to say, not be targeted for assassination without trial, ensuring that habeas corpus only be suspended for something the public actually considers to be a full-blown war, and then only for clearly defined, time-limited purposes even for non-US citizens
... When you break out these books, the rights progressives and libertarians agree on are many, varied, easily definable and would hold immense popular support.