In the standard emission problem, each country's ruling party decides on an optimal level of emissions by analyzing the cost and benefit to the country. However, such policy decisions are often influenced by political parties' incentives to be elected. Voters tend to give higher priority to economic issues than they do to environmental ones. As a result, political parties have additional incentives to reach a critical economic benefit level, at a cost of higher emission level, in order to satisfy voters' expectations in economic issues. Therefore, this study explores the implications of political parties being averse to insufficient economic performance relative to a critical economic target level on sustaining an international environmental agreement on emission levels. In doing so, we allow countries to have asymmetric concerns about economic targets, as well as asymmetric technology levels. We find that stronger concerns about economic targets deter the most cooperative emission levels countries could jointly sustain. Furthermore, technological asymmetry could either deepen or offset this impact. These results suggest that efforts on achieving substantial international environmental agreements should be supported at the citizen level to eliminate the adverse effects.