It would have a high chance of backfiring. People tend to get pretty mad if someone kills a high-ranking politician, especially a president, because he's not just a politician but a symbol of the country itself. So if your sleeper pulled off an assassination, you would have to take into account not just whether it succeeded, but whether there would be a backlash of pro-conservative sentiment following the assassination. The chances of that should be increased the higher the politician's rank was, the less conservative the politician was, the more conservative public opinion was, and in the case of the President, the approval rating. You should have to get the approval rating very low--20% or lower--to avoid swinging public opinion back toward conservative. It would be a lot like the way you can "alienate the masses" or "alienate everyone" during infiltration.
Honestly, though, I don't think the game should allow you to actually assassinate the president. The extreme difficulty of that sort of thing makes it pretty unrealistic for a ragtag group like the LCS to pull off. Part of the charm of the game is that anybody really can get killed with a lucky bullet to the head, no matter how good they are at dodging; so at least some realism seems to be desirable. And since we've already got them handily fighting off police sieges and laughing at the National Guard, I'd think you wouldn't want to add any more over-the-top stuff. If there were assassinations, I think they ought to be limited to judges and Congress and things like that. Leave the President and the Supreme Court to the Elite Liberal Amendments. After all, by the time public opinion would accept an assassination, two-thirds of the states would be okay with kicking out the president and the supreme court, so there wouldn't be any need for one. Plus, think of the way the presidential succession goes if the President dies--you get the VP and then the secretary of state, both of which will usually match the president's politics.
I like the idea of being able to disrupt a trial by having a sleeper shoot the judge. That would be a great way to use sleepers who come from places that aren't useful to you, like the University District or Downtown or whatever. Taking out members of Congress should be possible as well (triggering an instant re-election if successful), but it should have the chance of causing backlash--making public opinion more conservative, reducing the public's opinion of the LCS, and possibly affecting issues like privacy or police regulation.