The cuts are part of a compromise package offered by President Barrack Obama to Republicans in an effort to balance the budget.
The 10 chanted, "No cuts to Social Security," and "Jobs not cuts."
After the short protest at Swalwell's office at 5075 Hopyard Road, the group went to meet with Swalwell's office staff.
The local organizer of the event, Frank Burton, said, "We met with Josh Huber, who's his senior staffer."
Burton called Huber noncommittal, adding that Swalwell has not issued a statement. Swalwell also hasn't said whether he'll sign a letter to Obama, signed by Reps. Mark Takano (D-Riverside) and Alan Grayson (D-Fla.), warning against cuts to Medicare, Medicaid and Social Security benefits.
The group also delivered a petition with 560 names that was begun by MoveOn member, Kevin Reynolds.
The Dublin congressman does support raising the ceiling on contributions, which could extend the date that Social Security would become insolvent, currently estimated to be 2033, according to Burton.
"Congressman Swalwell opposes any cuts to Social Security. In order to ensure the long-term viability of Social Security, he believes we should raise the cap on wages subjected to Social Security tax," said Allison Bormel, Swalwell's spokeswoman. "As a policy Congressman Swalwell does not sign pledges. A 'no-pledge pledge,' he likes to call it."
Obama doesn't actually plan to cut the program; his plan calls for smaller cost-of-living increases, beginning in 2015.
Some, including U.S. Sen. Nancy Pelosi from California, said not increasing the amount people receive is the same thing as a benefit cut.