Here are some of their thoughts.  A more complete listing of their proposals is at The Dailey Caller:

Reinstate and strengthen a prospective federal ban on assault weapons: These weapons are designed to fire a large number of rounds in a short period of time.  They constitute a lethal threat to law enforcement and other first responders.

This is…foolish.  There is no such thing as an “assault” weapon, other than a carefully manufactured-by-legislation definition.  Not even the military has “assault weapons.”

Moreover, the threat to law enforcement and first responders from this sort of mythical weapon, or the semiautomatic rifles on which this mythology is purported to be modeled, is far less than is the threat of pistols, knives, clubs, fire (especially when responding to arson fires), drunk drivers, and so on.  This excuse fixes a nonexistent problem.

Reinstate a prospective federal ban on assault magazines: These magazines hold more than ten rounds and allow a shooter to inflict mass damage in a short period of time without reloading. Banning them will save lives.

This, too, is nonsense.  There is no such thing as an “assault magazine,” other than a carefully manufactured-by-legislation definition.  Here, too, even the military has no such things.

Moreover, the threat to lives from these artifices pales compared to the real causes of killings, some of which were enumerated just above.

Both of these, also are useful—critically so—in allowing private citizens to defend themselves.

There are these, too:

Require a background check for every gun sale, while respecting reasonable exceptions for cases such as gifts between family members and temporary loans for sporting purposes: It is estimated that four out of ten gun buyers do not go through a background check when purchasing a firearm because federal law only requires these checks when someone buys a gun from a federally licensed dealer.

The rest of this item is a red herring; I’ll ignore it here.  Four out of ten sales don’t go through a background check because they’re private sales from one citizen to another.  With the cost of a background check running to hundreds of dollars, this serves only to suppress those private sales.  On top of this, requiring a background check for a private sale represents an atrocious invasion of privacy for the purchaser by the seller—even if the seller has no intention of the invasion other than an arbitrary, superfluous law requires it.

Strengthen the National Instant Criminal Background Check System (NICS) database: Immediate action is needed to ensure the information in the NICS database is up to date.  Many federal and state agencies remain deficient in transferring important records to the database.

No.  This is simply Progressives demanding government compile dossiers on honest American citizens on the off chance that a small number might prove unsavory.  This is nothing more than a presumption of guilt without due process—without even probable cause.  The United States isn’t France.

Some of their thoughts are on the right track, though.

Pass legislation aimed specifically at cracking down on illegal gun trafficking and straw-purchasing: Straw-purchasing is when a prohibited buyer has someone with no criminal history walk into a gun store, pass a background check and purchase a gun with the purpose of giving it to the prohibited buyer.

Nice idea, but it’s not necessary, and we already have too many mostly redundant laws on the books.  And the areas of non-overlap are nothing more than sources of confusion and litigation.  Moreover, this is a law honored in the breach, as DoJ’s Fast and Furious illustrates.

Prosecute those prohibited buyers who attempt to purchase firearms and others who violate federal firearm laws: Federal law bars nine categories of people—including felons and those prohibited because of mental illness—from buying guns.

Absolutely, enforce the laws on the books, including applying the sanctions the laws supply.

Close the holes in our mental-health system and make sure that care is available for those who need it: Congress must improve prevention, early intervention, and treatment of mental illness while working to eliminate the stigma associated with mental illness.

This is on the right track, but government involvement must be absolutely minimal.  In the Soviet Union, the government defined disagreeing with the government as a form of mental illness.  We don’t need the USSR’s gulag reborn here.

Support responsible gun ownership: Congress should support safety training, research aimed at developing new gun safety technologies and the safe storage of firearms.

Certainly. As soon as Congress has reformed our tax code to simplify it and lower rates in parallel with greatly reduced Federal spending, so our economy can finally recover and we as a nation can afford this sort of expenditure.  At that point, Congress should begin jawboning with the States to do this sort of thing.

Given the active interference with individual freedom and responsibility represented by those first few items, though, I have to ask: what problem are the Progressives actually trying to solve—disarming the population they wish to govern, or reducing violence?