Thirty-year bond yields wobbled around 2.91 percent after closing at 2.868 percent Monday.
On the data front, the pace of growth in the U.S. services sector rose to a five-month high in April, lifted by a surge in business activity.
the Institute for Supply Management said its services index rose to 57.8 last month from 56.5 in March. Analysts were looking for a reading of 56.2, according to a Reuters survey. The April reading was the highest since November.
In a separate report, the Commerce Department said the deficit on the trade balance jumped 43.1 percent to $51.4 billion, the largest since October 2008. The percent rise also was the biggest since December 1996.
The rest of the week includes reports on jobs, with the ADP national employment report; weekly jobless claims; and finally the Labor Department's non-farm payrolls report for April on Friday.
Yields on the 10-year Treasury were just off its seven-week high on Monday, hitting 2.14 percent amid low volumes and after a report showing new orders for U.S. factory goods had their biggest increase in eight months in March.
—Reuters contributed to this report.