There are a number of attacks on HTTPS in practical use, that the NSA probably or plausibly has:
Given the number of CAs in the world, it is pretty well certain that some of them are either knowingly or unknowingly subverted by the NSA. It would be very hard to rule out that one or more of the organizations trusted by browsers are actually NSA founded and operated. So most likely the NSA can issue itself certificates for any domain it pleases, in any name it please, that your browser will accept. Even if you check the name of the organization in the browser address bar, you probably don't check that the issuer is "the right one" for your bank. That's kind of what certificate pinning is about.
Heartbleed. The NSA may well have known about it up to 2 years before the rest of the world, which would mean that a hefty proportion of sites were subject to leaking their admin passwords and/or certificate private keys. In some sense heartbleed is over now, but not every site that was possibly vulnerable has revoked its old certificates, and it's a warning that show-stopping flaws can be undetected for years. There could be more.
Hacking operations. The NSA can throw every attack in the book at a server, plus some attacks only in its own secret books, in attempt to control the machine or acquire its private key. The same goes for the client. Of course this doesn't necessarily lead to an attack "on HTTPS", it might capture/control the decrypted traffic, but it still means that HTTPS does not imply "hidden from the NSA".
Physical operations. I suspect this is rare overall, never mind incredibly unlikely to be used on you or me, but the NSA can send guys to do stuff. As can related organizations such as the CIA or law-enforcement. The FBI and US Attorneys have shown in the past that they're prepared to accept intelligence from spooks in criminal cases and lie to a court about its source. It seems likely to me that under extreme circumstances they would be equally prepared to perform ostensibly criminal acts to enable NSA surveillance. An overseas CIA operation to do likewise probably wouldn't even be a crime in the US. Naturally it might well be a local crime, but breaking local law is kind of the point of the CIA ;-)
The NSA has the most effective known man-in-the-middle capacity. It has, as it were, its own boxes in the major internet routes: undersea cables, ISPs and suchlike. According to some of the Snowden documents it has working systems to actively intercept connections between specified endpoints. This alone is not sufficient to break HTTPS of course, but combined with factors above it means that whatever keys they obtain do translate to practical attacks.
The article you link to talks about Bullrun and other related programs. The fact that the NSA takes multiple approaches suggests that they don't have an all-purpose point and click break of SSL or its algorithms, at least not one that's cheap and practical to widely deploy. It's difficult to really understand the NSA's strategic assessments, but one might think that if they had that then they wouldn't need to take the risk of collaborating with big internet companies on specific subversions. Bruce Schneier (and probably others) has highlighted documents that refer to a trade-off performed by the NSA to judge whether a particular target is valuable enough to justify using certain attacks, especially attacks whose frequent use would tend to lead to them being discovered. I forget the details.
You can argue that "stealing someone's private SSL key" or "becoming a CA" isn't "an attack on HTTPS", but it really is for what lay people usually mean by "HTTPS". It's not an attack on the algorithms used, but HTTPS isn't just the algorithms, it's the whole system. Including the rather sprawling key distribution mechanism.
Whether HTTPS is a solution for secure web-browsing is another matter. If you're a US citizen, then your duly elected government has determined that it is perfectly "secure" to have your internet traffic observed by the NSA. Indeed, more "secure" than allowing the bad guys' traffic to be unobserved. The definition of "bad guys" is widening now that the NSA doesn't address itself solely to foreign threats as originally mandated, but also to domestic security and criminal concerns. The same applies in other countries, especially those close allies of the US who share intel with the NSA. Wooo!
It's relatively unlikely that the NSA cares about you or me in particular. Based on what we've seen of the Snowden documents it's relatively likely that if they can intercept and decrypt a particular piece of traffic with minimal marginal effort, then they will, and as such it seems likely that a good proportion of innocuous HTTPS traffic is not "secure". Naturally most of that data never reaches a human analyst, but it's available.
For me the significance of the Snowden documents wasn't that any techniques in it left people thinking, "that's amazing, we never knew that was mathematically possible". AFAIK no specific cryptographic techniques have been revealed. The news was the confirmation that the NSA has worked itself far into the infrastructure, so that security fails even without a genuine "cryptographic break".