The press corps’ relentless focus on the assault weapons ban — and its dim prospects in Congress — have created the misleading impression that Obama’s whole gun package is dead on arrival in Congress. As I keep telling you, the universal background check is arguably more important — and it has a decent chance of becoming law.

But beyond that, there’s still another major provision of Obama’s gun package that also has a shot — and it will be introduced in Congress this week with bipartisan support.

I spoke this afternoon with Senator Kirsten Gillibrand of New York, who will introduce a measure tomorrow or Wednesday, with GOP Senator Mark Kirk of Illinois, that would impose much more serious penalties on so-called “straw purchasers” who currently get little more than a legal slap on the wrist for buying and reselling guns to those who fail background checks. Gillibrand believes this will be a very difficult proposal for Republicans to oppose, since it is designed only to target gun sales that are explicitly all about putting guns into the hands of those who presumably shouldn’t have them, having failed background checks.

“This piece is bipartisan already,” Gillibrand told me. “I think it has a great chance of success, because it doesn’t affect law abiding gun owners at all.”

Crucially, Gillibrand said she will be calling for a straight up or down vote just on this proposal. Just as a vote only on the universal background check piece would do, this will force Republicans — and red state Dems who are reportedly skittish about gun reform — to take a position directly on something that is only about keeping guns out of the hands of those who don’t have them. “Eighty five percent of weapons used in crimes in my state come from out of state and 90 percent of them are illegal,” Gillibrand said.

Pressed on whether the House GOP would really allow a vote on this provision, given GOP hostility to gun regulations, Gillibrand insisted it would, given that it should be a no brainer: “It’s a bill that can be significantly bipartisan.” She even said Kirk has been reaching out to some House Republicans to gauge support.

If Obama were to get universal background checks and this gun trafficking measure approved — a big “if,” perhaps, but significantly more likely than getting the assault ban — the President will have achieved roughly two thirds of his gun agenda. “I support the assault weapons ban,” Gillibrand said, but getting those two proposals through would be a “huge deal” and a “tremendous step forward.”

One other point: The relentless focus on the assault ban has allowed lawmakers to dodge the difficult political question of whether they really oppose the package’s less controversial no-brainer proposals: The universal background check, and the anti-trafficking measure. Hopefully, when this latter proposal gets introduced, lawmakers will be asked to take a stand on it. Hopefully.