Complex sentence: One of President Garfield's more wearying duties was seeing office seekers, and he saw Guiteau at least once, suggesting that Guiteau approach Blaine, as the consulship was within the Department of State.
Split into simpler sentences: One of President Garfield's more wearying duties was seeing office seekers, and he saw Guiteau at least once. White House officials suggested that Guiteau approach Blaine, as the consulship was within the Department of State.