I'll cut and paste the relevant part from the multi administration answer that I just posted here; in short, it wasn't Grant but Johnson.

Andrew Johnson had tried to get Grant on his side in his battles with Radical Republicans in Congress, even forcing him on the campaign trail before the 1866 elections (and that was such a dismal failure that Democrats later claimed Johnson's performance had lost their ticket something like 2 million votes.) But impeachment changed things; interestingly enough Thaddeus Stevens was so keen on doing so even before Johnson had walked into the trap of the Tenure of Office Act that he tried to get the House to impeach Johnson with blank articles of impeachment to be filled in later, tried to do so again even after the conviction failed, and in a two year period there were something like 7 attempts. The most important aspect to this, though, was the actual one that stuck was because of Edward Stanton refused to relinquish his office, and Johnson - who thought he was vastly better at politics than he was - attempted to put Grant in the middle of it by appointing him as War Secretary instead. Despite not much liking Stanton and later even asking him to resign to stop the chaos, Grant saw through this (along with at least one attempt to send him overseas as an ambassador), and at that point Johnson properly saw him as his main potential rival in the 1868 race. Grant accepted appointment as interim War Secretary instead, worked with Congress on trying to maintain military districts in the South and Reconstruction, refused to let Johnson trap him into a potential violation of the Tenure of Office Act (and $10,000 fine which Johnson offered to pay for!), and once Stanton was reconfirmed actually walked out of a Cabinet meeting since he refused to continue reporting as War Secretary. This led to bitter battles with several other members of the Cabinet where Grant actually never spoke to several again, and in turn Johnson by early 1868 viewed Grant as an outright traitor and the two at times refused to appear together. Grant refused to attend the 1869 New Year's reception at the White House, Johnson made several last minute appointments that he knew Grant would despise, Grant scuttled a treaty agreement that might have aided Southerners, and when the Cabinet met on Inauguration Day, they had expected to ride to the ceremony together (another source suggests separate carriages) - but when Grant arrived, Johnson shook hands with each of them and surprised them by departing elsewhere in his own carriage.