If by possible is meant routes that are actually getting some serious consideration by the states, there are a few. I would not call all of these likely, but at least with some possibility of moving forward. Just out of the top of my head:
LA-SF High Speed Rail - it is still alive, and at least part of the system will probably be built. The full one:
hboy:
Northern Lights Express MSP-Superior
BOS-Montreal via Springfield/Vermonter route.
LA-Coachella Valley/Indio has seen a bit of movement, but UP resistance has to be overcome.
Heartland Corridor extension (I know NE will be a hard nut, but so far the planning process has been moving forward)
The privately funded Desert Xpress seems to be soldiering on too...
I was looking at Amtrak corridor services that will be and might be started within 4 to 5 years. The crystal ball gets very cloudy for 10 years out. Given the reality of lead time for planning, EIS, lining up the funding, if the plans and support are not far along, the service won't start in 5 years. The CA HSR and DesertXpress proposed systems are true HSR and would very likely operate separately from Amtrak. Besides the CA HSR central valley section will be under construction in 5 years if nothing stops it, but is likely 8-10 years away from any service. DesertXpress is the wild card, since they are a private company and thus can build more quickly, has jumped through the many hoops of federal & state approval, they could actually be running by the end of 2016.
-Northern Lights Express in MN: received federal funding this year for engineering and environmental studies. Don't know how much work is needed and what it will cost to start the service. Strikes me as unlikely within 5 years. If federal funding is available, then within 10 years is a better bet.
-Boston to Montreal: I think this can happen, but if it depends on double track restoration and track upgrades from BOS to Springfield, AND new single level coach cars, hard to see it happening in 5 years.
-LA to Coachella valley/Palm Springs: a $400K study is supposed to start soon for this possible corridor. If UP's demand are reasonable and the main work to be done is to build new stations, could happen in 5 years, but also is likely to have to wait until CA gets all the new bi-level cars delivered.
CO - front range corridor
TX - Austin-San Antonio
I know the latter (and maybe the CO service too?) is technically considered a commuter rail, but the length and a few other features makes it somewhat intercity-flawoured...
There are commuter and longer range commuter corridors that can benefit Amtrak, in much the same way as Amtrak operated state supported corridor services. SunRail in Orlando and central FL will fix up 61 miles of track with restoration of double tracking and renovation of the Amtrak stations on the route. The Silver Star and Meteor could see ridership increases due to SunRail.
New York-Scranton-Binghamton - I have no idea if this has seen any movement to get onto the real drawing board, but it is three pretty rail friendly states.
Finally Quad Cities - Iowa City has not been decisively nixed yet, and there's a slim chance it still might go through. If it does and proves successful, an extension to Des Moines is then not unlikely a few years later on.
On top of this the High Speed and stimulus funds did give quite a few grants for various preliminary studies. Whether any of these will gain any traction when finished is anybody's guess. At least it will need a new round of federal spending to get the actual projects going.
-New York-Scranton-Binghamton: I think NY's and PA's attention are focused elsewhere. NY state on the Empire corridor, PA on the Keystone Corridor. I suspect plans for restoration of service over the Lackawanna cutoff will sit on the back burner until upgrades to the Empire and Keystone corridors are much further along.
-Extension from Quad Cities to Iowa City and then Des Moines: I don't think this is dead at all in the longer run. With the funding in place for Chicago to Quad Cities and to buy the rolling stock, the barriers to extension to Iowa Cities will be much lower. Even if the current Governor & legislature squash the project, once the service starts to Quad Cities and if it is seen as successful, then extending the trains further into Iowa will get increasing political support.
All those grants for feasibility and engineering studies will help lay the foundation for future expansions. I look at the studies as similar to planting seeds. Some won't grow and won't lead to anything. But some will and eventually lead to new corridors getting started.