If West Ham can win 4 in row then it it is quite possible United can also, I agree they look very poor under Moyes but stranger things have happened in football.
Their next 4... West Brom Away, Liverpool Home, West Ham Away, Man City Home
I'm not sure they will win all four of those. And they would probably need to do that, and have us drop in 2 games to have the gap surmountable with 7 games to go.
With the Sunderland game having moved, our next four is difficult to be fair. Southampton Away, Man U Away, Cardiff Away, Tottenham Home.
Say we draw all four of those games. The most Man U and Tottenham could get out of their runs of four games is 10 because we stopped them winning one of their games. 10 minus our 4 points means at best a 6 point gain on us (by winning all their others). And would need to beat Man City for Man U and Chelsea/Arsenal for Spurs. To be level with Spurs and 5 ahead of Man U with 7 games to go.
Alternatively, we win two of the games, and lose the ones to Spurs/Man U - they can gain 12 points on us, but with our 6 the most they can gain is 6, same as above - which is level with Spurs and 5 ahead of Man U again.
Essentially, a win against Spurs and a draw vs Man United probably seals it for us, barring utter collapse.
Because if you beat Spurs, the most they can get out of those 4 games is 9, minus the 3 points we took against them, is 6- assuming we lose all THREE of the others.
I think it would be realistic to say Cardiff and Tottenham are wins, Man U is a draw, Southampton a loss say. That gives us 7, the most Man U can gain on us is 3 points in that scenario (winning the rest of their games) and the most Spurs can gain is 2.