Don't know, but here are a few things to consider.
If memory serves, at one time there was some question as to whether or not I-49 would even run through Texas. This would have required all southbound traffic to proceed to Texarkana, Arkansas to access I -30. Since the proposed route crosses into Texas, TxDOT can build its own connector to I -30 on their side of the state line (think commerce and economic development here), but in order to do so would have to provide the contiguous I-49 connection back into Arkansas.
All that to say, the prevailing thought is each state will pay its own way. But anything can happen. One never knows when a $2 Billion+ earmark will surface. 
A cryptic quote, AHTD! Me hopey, to paraphrase an old saying.

(And AHTD, let me modify this. Somewhere on this forum there's a picture taken from a PowerPoint
Texas Department of Transportation presentation, used by a
Shreveport television station, showing the key corridor (from Canada through the central U.S. to both Mexico and (the nation's largest ports on) the Gulf of Mexico) that will run through
Arkansas with a completed I-49.
I've only lived in northwest Arkansas since 2002, but old-timers here tell me how long the not-for-long-named I-540 took to build. But that was
before I-49 dropped all the way from Kansas City to just above the Arkansas border. And
before I-49 was extended north all the way to Texarkana as is about to happen in a matter of a month or two. And
well before Texas became America's second most populous state, and started to build its section of I-69 which will give both Houston and the Lower Rio Grande Valley (as well as the Texas ports in America's "top 10 biggest ports") access to a lot of markets. And, frankly,
before Northwest Arkansas became "home" officially to the world's largest company and, as of this summer, 800,000 people between that region and its neighbor Fort Smith.
My guess (and though I know you see it too you're not privvy to say how much yet, that's for us to find out through you later) is that there are a LOT of people all over the place now (as opposed to way back in "Y2K") who have a GIGANTIC interest in seeing a completed I-49. I used elsewhere the analogy that I-49 is closing in on our state like the pincer of a huge crab (bad analogy as a crab uses such to break things, and I-49 will BUILD, a lot, of things). The announcement of the resignage (sic?) this week will make the claw close just a bit more. And with every mile said "claw" closes, said "LOT of people" (including those who hold some significant pursestrings) will take even more notice.)