Stock futures fell on Sunday as the U.S. government remained shut down.

Dow Jones industrial average futures declined 33 points and briefly fell as much as 101 points. S&P 500 and Nasdaq 100 futures dropped 2 points and 8 points, respectively.

The U.S. government shut down Saturday after a bill that would've kept government funded through Feb. 16 was voted down in the Senate. The shutdown will continue for a third day after the Senate on Sunday failed to reach an agreement to break an impasse before the work week began in Washington.

The White House was quick to blame Democrats once the shutdown started. In a statement, White House press secretary Sarah Sanders said: "This is the behavior of obstructionist losers, not legislators."

On Sunday, however, Republican lawmakers were getting behind a plan that would keep the government funded through Feb. 8. Meanwhile, some Democrats are preparing to give immigration concessions to the GOP.

Some of those concessions include President Donald Trump's proposed wall along the U.S.-Mexican border. A point of contention between Republicans and Democrats is an immigration bill which Democrats want to pass.

This is the first U.S. government shutdown since 2013. That year, the government was shut down for 16 days.

Concerns about a shutdown kept investors on edge last week. On Tuesday, the Dow gave up a 283-point gain, while the S&P 500 and Nasdaq also closed lower in that session. The Cboe Volatility index (VIX), widely considered the best fear gauge on Wall Street, finished the week nearly 11 percent higher.

Historically, the Vix averages a return of 9.7 percent one week after a government shutdown, while the slips 0.3 percent in that time period.

—CNBC's Jacob Pramuk contributed to this report.