Is positive self-talk beneficial for those with low self-esteem? According to the paper Positive Self-Statements: Power for Some, Peril for Others by Wood (2009) positive self-talk is beneficial when the person has a reasonable level of self-esteem in the statement, but harmful when they don't. The PsychCentral article, "Got Low Self-Esteem? Don’t Ditch the Positive Self-Talk Just Yet" by Summer Beretsky points out a few issues with the methodology:


Limited sample size
Short "bursts" rather than more concentrated time to convince themselves
Not controlling for whether they believe in the statement they are proclaiming


Are there any other studies that deal with these issues?


Wood, J., Elaine Perunovic, W., &amp; Lee, J. (2009). Positive Self-Statements: Power for Some, Peril for Others Psychological Science DOI: 10.1111/j.1467-9280.2009.02370.x
Just to be clear, Wood et al (2009) summarise their propositions on page 861:


  Thus, we propose that positive self-statements have the potential to
  make one feel worse if they lie outside one’s latitude of acceptance,
  are self-discrepant and thereby highlight one’s failures to meet one’s
  standards, and arouse self-verification motives. We further propose
  that positive self-statements are especially likely to backfire for
  the very people they are meant to benefit: people with low
  self-esteem. Such people, by definition, see themselves as failing to
  meet standards in more domains or in more important domains than do
  people with high self-esteem. Moreover, self-verification motives
  should bias people with low self-esteem to reject positive
  self-statements, but encourage people with high self-esteem to
  accept them.


In the literature review, Wood et al cite several articles related to attitude formation and self-relevant feedback. They mention one particular study, where


  Eisenstadt and Leippe (1994) asked participants to identify a trait
  they would like to possess but believed they lacked. When Eisenstadt
  and Leippe later told participants that they actually did possess that
  ideal trait, participants felt worse, rather than better.


References


Eisenstadt, D., &amp; Leippe, M.R. (1994). The self-comparison process
and self-discrepant feedback: Consequences of learning you are
what you thought you were not. Journal of Personality and Social
Psychology, 67, 611–626.
Wood, J., Elaine Perunovic, W., &amp; Lee, J. (2009). Positive Self-Statements: Power for Some, Peril for Others Psychological Science DOI: 10.1111/j.1467-9280.2009.02370.x