When President Barack Obama heads to Connecticut on Monday, it will have been 115 days since the massacre at Sandy Hook Elementary – but just four days since the state legislature enacted what looks to be the strongest gun control law in the nation.

The timing, and the bipartisan but balky way the lawmakers in Hartford responded to the mass killing 40 miles down the road, suggests there’s still a window for some sort of comprehensive gun violence package to get through Congress. But the aperture is only a small one, and already it’s certain the federal legislation won’t be as broad as what Gov. Dannel P. Malloy signed on Thursday, what’s already been enacted in Colorado and New York, and what may get on the books this spring in Maryland.

What’s especially instructive about Connecticut’s new statute, though, is how 16 weeks of intensive bargaining, with concessions on all sides, produced a package that secured the sort of broad bipartisan backing so rare at the Capitol these days.

The bill got the votes of seven out of every eight Democrats in the General Assembly — suggesting the small share of the party’s legislators from “red” districts were given a pass to vote “no.” It was also supported by two out of every five Republicans — suggesting the limits of the lobbying muscle flexed not only by the six firearms manufacturers in the state, which threatened to take their 7,300 jobs out of state if the measure advanced, but also by the National Rifle Association, which has seen a surge in membership in Connecticut as elsewhere since the Newtown murders.

If the precise levels of support from each of the four caucuses in Hartford were applied to Congress, the package would be on course to pass with 69 votes in the Senate (even with five Democrats opposed) and 267 votes in the House. Even after discounting for the fact that politicians from both parties in Connecticut are generally more liberal than their elected counterparts in the rest of the country and for the fact that the state was the location of Adam Lanza’s horrific school shooting rampage, the numbers still indicate a theoretical majority is available in Washington for a multifaceted gun control bill.

That’s especially true when remembering that what Connecticut has just enacted goes well beyond what’s on the table in Congress. The state has just banned new sales of a specific roster of semiautomatic rifles — the sort of assault weapons ban on which Obama and Senate Democrats have already essentially conceded defeat. And the new law will create the country’s first statewide registry of people convicted of gun crime, require people who already own large-capacity ammunition magazines and assault weapons to register them and mandate new “eligibility certificates” for purchasers of many weapons — the sort of record-keeping requirements that are proving so difficult to get off the ground in Congress.

In fact, what those big majorities of lawmakers in Connecticut just endorsed and the roster of what Congress will consider share is only these major provisions: a background check system for private transactions and at gun shows, a ban on new sales of ammunition clips holding more than 10 rounds and modest funding to improve school security.

In other words, members of Congress are being asked to consider something much less dramatic than what members of the Connecticut Legislature just embraced. But they are being asked to get the ball rolling at the same time — before public sentiment for bold gun control looks to start fading.

Two polls out this week found still-overwhelming support for expanded background checks, 87 percent in an MSNBC survey and 91 percent in a Quinnipiac University poll. But that survey showed a surge — to 48 percent — in the number worried that such checks could lead to government confiscation of legally owned weapons.

Such numbers reinforce that the window of opportunity in Washington for gun control advocates could become impossibly narrow in a matter of weeks. Which is why Obama is keeping up his public and private lobbying and why his latest road trip is planned for Monday, just as the Senate starts a debate on gun violence legislation, probably lasting 10 days. Whatever senators can agree on in that time will be the high-water mark for gun control advocates; the House is sure to reduce the scope of whatever the Senate sends its way.

If there’s an impasse in April, in the afterglow of what just happened in Hartford, it’s tough to see how the momentum gets restarted.