The provided sources overwhelmingly and consistently support the statement. Multiple high-authority news outlets and primary government sources directly link a legislative conflict over immigration policy to the risk of a government shutdown. Several sources explicitly identify a funding deadlock for the Department of Homeland Security (DHS) as the central issue. Reports from CNN, Al Jazeera, and PBS NewsHour detail how Democratic demands for reforms related to Immigration and Customs Enforcement (ICE) are being met with Republican pushback, creating an impasse in negotiations for the DHS spending bill. This directly establishes the 'legislative deadlock on immigration' part of the statement. Furthermore, these sources, along with others, explicitly connect this deadlock to the risk of a government shutdown. One report notes a shutdown is 'becoming more likely' due to this specific dispute, while another mentions the 'risk of a shutdown' ahead of a funding deadline because of disagreements over immigration enforcement. Primary sources from Congress.gov corroborate the existence of a legislative deadlock by documenting the use of continuing resolutions to temporarily fund the government, including immigration programs. While some sources, like the Congressman's website and the Air Force news release, only confirm that a shutdown is a recognized risk without specifying the cause, they do not contradict the other evidence. No sources offer a conflicting reason for the shutdown risk. The cumulative evidence from both primary and secondary sources provides a strong, direct, and consistent case for the statement's truthfulness.