As a matter of political tactics, I think the Christian Science monitor is wrong when they opine:
And even the CRA has a downside. It must be used wisely or it may do more harm than good. For one thing, once the CRA has been used to repeal a rule, the agency cannot reintroduce a modified rule on that issue, potentially leaving legislative and enforcement gaps, de Rugy notes.
Newt Gingrich wrote the CRA and he knew what he was doing. He wanted the effect of using the CRA to be to permanently bar future reversal through future executive orders by default. If this was not the intended outcome it can be reversed through a followup bill.
So lets say that Clinton had issued an executive order protecting Yellowstone from logging, if Dole had won the GOP could then have used the CRA to reverse the order and permanently prevent a President from issuing a new one.
The CRA only requires a simple majority and cannot be filibustered. If Congress decides to use a single vote to reverse multiple rules the courts are barred from reviewing the procedure employed. There is no forum where the procedure can be disputed, ergo one vote to disqualify all the rules in one go is fully possible.
So the Republicans have no ability to oppose rule reversals under the CRA and questionable incentive to filibuster a subsequent bill to restore executive rulemaking power. On the contrary, they are more likely to be in favor than the Democrats.
If Bush issues an executive order to gut the clean air act, the Democrats use the CRA to reverse it and the clean air act is safe from future Republican presidents. If the reversal limits Obama's scope to use the clean air act proactively they use their 58+ seats to push through a new bill.
But in practice the Democrats won't use the CRA because they don't need to. Having established that the Democrats have the upper hand tactically, there is no incentive for the GOP to attempt a filibuster as the Democrats can inflict an even worse outcome from their point of view with no need for cloture.