When something squeaks by, it is narrowly passing between obstacles. There are objects that will literally squeak when they are squeezed between two objects, such as a simple child's balloon. From this arises the expression, to squeak by.
Example: Headline: Barack Obama's tax plan could squeak by with GOP help
Note: "GOP" stands for "Grand Old Party," a nickname for the Republican Party. It is used by journalists because it is only three letters long and, therefore, saves space. (It's true!)