Question

how do congressional leaders influence legislation in Congress

Answer 1

members sometimes sponsor legislation at the request of the president.

The politicians that served in our country often ask for favors from other politicians  by using leverage of something that woulld be beneficial for that other politicians in the future and president could influence the decisiin as long as it does not repelled by 2/3 majority.

Answer 2

Congressional leaders in the United States government are able to influence legislation in congress because they have the ability to decide which bills will go out to be approved/denied on the floor of congress, and because they have leadership and control of the electoral support.