The separation of powers should ensure compromise but if a president is unwilling to do so then congress becomes more entrenched too. For example, Trump and congress had a very antagonistic relationship, one which landed then a shutdown of 35 days
Relationship with Supreme Court
Less challenging as they can nominate whoever they want, but vacancies don't appear due to the presidents will. Obama criticised the SC in his 2010 State of Union Address over Citizens United v FEC ruling as they had 'opened the floodgates' on spending
Limitations on the power
Approval ratings e.g. Trump had lowest at 34% and never got above 50%
Presidential mandate e.g. Obama got 365/538 electoral college votes alongside 52% of popular vote. Trump only won 304 and lost popular vote by 1 million
National circumstance: times of crisis impact approval. e.g. Bush had 90% after 9/11 but 38% after Katrina. Clinton was accused of lying under oath during Lewinsky scandal, nearly being impeached embarrassed him