(Corrects day in paragraph 1) * Futures down: Dow 0.40%, S&P 500 0.45%, Nasdaq 0.35% Dec 8 (Reuters) - U.S. stock index futures dipped on Tuesday as surging coronavirus cases threatened to further hamper a slowing economic revival, while investors waited for progress in ongoing negotiations for a fresh COVID-19 relief package. Most residents in California, the nation’s most populous state, faced new restrictions on Monday after record case numbers and hospitalizations, while officials in New York warned similar restrictions could come into effect soon. Nationwide, COVID-19 infections are at their peak, with an average of 193,863 new cases reported each day over the past week, according to a Reuters tally of official data, and health officials warned that the worst is yet to come. The S&P 500 and the blue-chip Dow fell on Monday, but the Nasdaq closed at record levels as investors returned to technology mega-cap stocks, which have thrived from the pandemic-induced shift to work from home. Positive developments related to the COVID-19 vaccine have in the recent past helped investors look past the surge in infections and raise bets on a swift economic recovery next year. That pushed Wall Street’s major indexes to all-time highs recently and the hardest hit cyclical stocks, which are more economically sensitive, have sprung to life after underperforming for most of the year. Market participants are closely watching whether policymakers will be able to clinch an agreement on a long-awaited COVID-19 relief bill and a $1.4 trillion spending bill, with Friday eyed as a possible deadline to avoid a government shutdown. The U.S. Congress will vote this week on a one-week stopgap funding bill to provide more time for lawmakers to reach a deal on both spending and pandemic relief. Pressure has mounted on policymakers to deliver a fresh infusion of aid to families and businesses reeling from the virus outbreak. Lawmakers enacted $3 trillion in aid earlier this year, but have not been able to agree on fresh relief since April. At 6:35 a.m. ET, Dow e-minis were down 120 points, or 0.40%, S&P 500 e-minis were down 16.75 points, or 0.45%, and Nasdaq 100 e-minis were down 43.5 points, or 0.35%. Among individual stocks, Tesla Inc fell 2.8% premarket after it unveiled plans to raise up to $5 billion in a share offering. (Reporting by Shriya Ramakrishnan in Bengaluru; Editing by Shounak Dasgupta)