Each branch has mechanisms to ensure the other ones do their job. The legislative branch can impeach and remove the President if he fails to execute the law; why can't the President hold Congressmen accountable for failing to do their duties under the law?
EDIT: Looks like he has that power specifically in the Constitution and it has been used in the past (sort of, just not the suspending pay part):
Article II, Section 3, Clause 3: Calling Congress into extraordinary session; adjourning Congress
The President may call extraordinary sessions of one or both Houses of Congress. If the two Houses cannot agree on a date for adjournment, the President may adjourn both Houses to such a time as befits the circumstances.
The last time this power was exercised was in 1948, when President
Harry S Truman called a special session of Congress. That was the twenty-seventh time in American history that a president convened such a session