What's needed right now isn't really manned launch capability, but unmanned launch, capable of docking and safe manned return, so they're not limited by the "best before" sticker on the Soyuz.
Let's see what the private brains come up with in the next month or two. Frankly, I'd be shocked if SpaceX and Virgin don't already have something mostly developed that fits the bill, since Musk and Branson aren't idiots, and would have seen the possibility of taking over ferry service to ISS and future projects long ago.
Virgin can only barely get above the Karman line, and they can't get near enough horizontal velocity to actually attain orbit. They're not going anywhere with SpaceShip1, near the ISS. Even if it had an IDS-style docking adapter.
Blue Origin isn't going anywhere with their suborbital New Shepherd hopper either. Same problems in a different shaped stack.
The only serious contenders able to reach the ISS with what is considered prototype or beta-acceptance hardware are SpaceX, Boeing, and Sierra Nevada. I'd really count SN's Dreamchaser as a more alpha-level product since I think it has yet to be mated to a booster... but I suspect the same could be said of Boeing's CST-100, too. Big difference there is Boeing/ULA make their own rocket and the Atlas team has been working closely with the CST-100 team, whereas SN hasn't been working with SpaceX or ULA regarding Dreamchaser as a payload. At least at a serious level.
One "could" also throw Orion into the mix (Lockheed's capsule that rides on the yet to be built SLS rocket). But no Orions are ready right now, and no SLS's are ready right now. A mock Orion rode on a Delta IV Heavy a few years back for high velocity reentry testing, but evidently the heat shield is undergoing modification after that particular test, so it wasn't particularly positive results there. Even if a DIVH is available somewhere in ULA's manifest and an Orion is ready, the re-worked heatshield hasn't been tested to prove humans can survive reentry in it.
There is a crew Dragon capsule at the Cape right now undergoing final integration checkouts. It's slated for Demo Mission 1 (DM1) in December or January.
Boeing was recently sent back to the drawing board with CST-100 due to some hypergolic fuel leak issues during a launch abort test a couple months back. That capsule isn't riding anywhere any time soon.
So, the only real possibility from the US front of any intervention, is from SpaceX. Dragon's heat shield is just an upgrade of the current cargo Dragon craft. It's thicker and designed for interplanetary reentry speeds, and a newer formulation of PICA-X that SpaceX has been using for cargo Dragon craft for years.
But, NASA being NASA, they would NEVER allow SpaceX's Crew Dragon to work as a lifeboat for ISS crew without a reentry test being done first. They'll de-crew the ISS before they rely on that.
Realistically, the only solution that's going to happen is as Cordex described: Russia will loft an unmanned Soyuz to replace the one currently up there. If there's a failure with that launch then crew will leave the ISS.
Which is a big back of suck for SpaceX, since they're in the lead over Boeing in delivering a crew vehicle to the ISS. There's a flag left up there from the last Shuttle mission, intended for receipt for the first company that builds a private vehicle capable of transferring crew. SpaceX has been waiting for months for a window to send Crew Dragon to the ISS. Boeing has behind the scenes pull that they are using to do a bunch of "paperwork-proofs" to demonstrate their capsule is manned-ready for its first demo mission, and NASA is considering putting a crew on Boeing's DM1 launch in spring of next year.
I've really been pulling for NewSpace to punch OldSpace in the nose over this one. It'd suck if Boeing gets that flag before SpaceX due to backroom favoritism and schedule manipulation.
ETA: I failed to express the collateral damage correctly. If ISS is de-crewed, then SpaceX cannot send their DM1. Contractually, the ISS must be crewed for observation and feedback purposes for the mission to be a success. As well as for emergency damage control in the event of malfunctions. So SpaceX's DM1 will be pushed back until Soyuz can put crews back up there. That pushes SpaceX further from their finish line, but Boeing can keep working their puppet strings behind the scenes to try and fly manned from the get-go.
