The increased settlement of Americans in the Oregon Country during the 1840s likely had an impact on negotiations with the British over the territory. The greater the American presence in the region, the more pressure they could exert on the British to cede control of the land to the United States.
The Oregon Trail was an essential part of the idea of Manifest Destiny, which was the belief that it was the United States' destiny to expand its territory across the continent. The Oregon Trail represented a route for American settlers to move westward and establish new settlements, further fulfilling the idea of Manifest Destiny.
The statement "The phrase 'Fifty-Four Forty or Fight' was a successful political slogan" is an opinion. Success is subjective and can be defined in different ways, so the statement cannot be verified as a fact. One person might view the phrase as successful for rallying support for American territorial expansion, while another might view it as a failure for leading to diplomatic tensions and the potential for war with Great Britain.