Detailed Analysis:

• Claim: Trump renews attacks on Obamacare in a new push over the government shutdown.
• Verification Source #5: Source 5 mentions Trump's conflicting statements about the future of Obamacare during his 2024 campaign, suggesting a continued focus on the issue.
• Assessment: Supported. The sources confirm both the shutdown and Trump's continued focus on Obamacare.
• Claim: The president claimed that the Affordable Care Act benefited insurance companies over people.
• Assessment: Unverified. None of the provided sources directly quote Trump making this specific claim in the context of the shutdown. While source 5 mentions his stance on Obamacare, it doesn't verify this specific statement.
• Claim: Trump said he would work with both parties on the issue “once the Government is open.”
• Verification Source #3: Source 3 indicates Trump's willingness to negotiate regarding the shutdown, which indirectly supports the claim that he would work with both parties once the government is open.
• Assessment: Partially Supported. Source 3 suggests a willingness to negotiate, but doesn't directly confirm the specific quote about working with both parties on Obamacare once the government is open.
• Claim: The government shutdown is straining US air travel.
• Verification Source #4: Source 4 states that United Airlines will cut about 4 percent of its flights through the weekend as the ongoing government shutdown strains US air travel.
• Assessment: Supported. Source 4 directly confirms the strain on air travel due to the shutdown.