Ireland will take over the presidency of the EU Council on July 1 and is expected to face challenges, including negotiating a new EU budget for 2028-2034.

The analysis of the claims reveals the following: Ireland's role in negotiating the new EU budget for 2028-2034 is plausible based on the evidence found. However, no fact-checks specifically verify this, but the task aligns with Ireland's upcoming EU Council presidency. The claim about the EU proposing a budget of nearly 2 trillion euros is supported by web sources, indicating a €2 trillion package that includes long-term and recovery budget components. Regarding the allocation of 166 billion euros for COVID-19 debt repayment, no direct evidence was found. Lastly, the claim about Cyprus proposing a compromise budget which was rejected was not confirmed in the evidence, though it shows a proposal was made. Overall, the topics discussed are complex, and further detailed evidence is necessary for absolute verification of some claims.