They control the House of Representatives, so they could strip the NSA of funding.
Also, they could actually investigate and push for prosecution of the wrongdoers [essentially the whole agency, plus contractors] — would that be a mess
or open a can of worms
? Quite possibly. However, it would also show that the Republican party isn't just all talk, and that it's willing to get into uncomfortable places to get rid of corruption — but they didn't, which shows that they accept the NSA's lawlessness, and approve of it.
Seriously, if they made a honest, vigorous push against it even if they were stymied by the Democrats (though I think the topic is so toxic even the Democrats wouldn't be able to stand against an honest opposition) they would garner support from the general population. It was seriously a no lose proposition for them (or even the Democrats, had they capitalized on the opportunity) — the non-action and de facto defense of the NSA shows [to me] exactly that these elites are unified in their statist ideology.
In the mean time, our choices are to give more power to the Democrats, or take what we can get.