Many Trump critics are delighted at the possibility that the 74-year-old might be charged, including activists at "Rise and Resist" who called for his imprisonment during a demonstration in New York in January.
Senate Democrats need to pass a budget resolution to unlock a legislative tool called reconciliation.
Most legislation must get at least 60 votes in the 100-seat Senate to pass. But the chamber is divided 50-50 and Republicans oppose the Democratic president's proposal.
Biden and his staff are also expected to present the Republican senators with details on how his COVID-19 relief package would benefit their respective states, a White House aide said.
After the 15-3 vote by the committee, Senate Majority Leader Chuck Schumer said the full Senate would vote on Blinken at noon EST (1600 GMT) on Tuesday.
Yellen on Friday sailed through with a unanimous approval vote in the Senate Finance Committee, indicating that she has enough votes to easily win confirmation.
A confirmation for former Federal Reserve Chair Yellen less than a week after Biden took office is quick by recent standards.
In prepared testimony at her confirmation hearing, Yellen said her task as Treasury chief will be to help Americans endure the final months of the coronavirus pandemic.
Neither the president-elect, nor I, propose this relief package without an appreciation for the country's debt burden.
Gold is seen as a hedge against inflation and currency debasement likely to result from large stimulus measures rolled out this year to cushion the impact of the pandemic.