There hasn't been any progress between the NFL and its locked out officials' union, and it appears the league is prepared to go on for quite some time with the replacements.
There were only a handful of officiating mistakes in Week 1 - most notably in the Seahawks-Cardinals game, in which the Seahawks were inadvertently given a fourth timeout late in the fourth quarter. And with the NFL digging its heels on the labor situation, the situation might not be resolved in the immediate future.
According to the Associated Press, the league has scheduled replacement officials for the first five games of the regular season. That doesn't mean they'll work that long, and if there is a breakthrough in talks with the union, the regulars will be back sooner than that. But it does indicate the league is prepared to go on as long as they have to.