The government shutdown is now the longest ever, and there are a variety of interesting implications. The first is that multiple economic reports will not be released as scheduled. The notable examples in the current week include Retail Sales and the New Residential Construction report (housing starts and building permits). An absence of econ data naturally increases uncertainty.
In and of itself, uncertainty is good for the bond market, but investors will still have access to a few other economic reports that could help form a consensus about what the economy might be doing. Of those, the only reports on this week's calendar with any market-moving history worth mentioning are the Philly Fed Index on Thursday and Consumer Sentiment on Friday. To put their past market-movement potential in context, it wouldn't be a surprise in the slightest if markets didn't react at all. But at least they provide a few "maybes" on an otherwise barren week for economic data.
The second implication of the record-setting shutdown is the fact that the fallout will become more and more relevant to the economy in ways we've never been able to witness. Investors will increasingly ask questions that hold future growth prospects up to the candle.
This has actually already begun to happen (because there hasn't been a compelling reason to expect this shutdown NOT to break records for several weeks now). As such, it is already benefiting the bond market. Conversely, any benefit realized by bonds due to shutdown-related uncertainty runs the risk of being abruptly unwound--at least partially--if an agreement is suddenly reached.