Democrats can do both.

According to https://www.congress.gov/crs-product/98-988:

The Constitution requires that a quorum, defined as a majority of the House, be present on the floor when the House transacts business. The House, however, always presumes that a quorum is present unless and until its absence is demonstrated conclusively. The rules of the House strictly limit the occasions on which a Representative may make a point of order that a quorum is not present. In current practice, Members usually make such a point of order only when a vote is taking place. If a majority of the Members fails to respond to a quorum call or participate in an electronically recorded vote conducted in the House, the House must adjourn or take steps necessary to secure the attendance of enough Members to constitute a quorum.

Since the House is always in quorum and Republicans have the majority, the House will always be in quorum. However, not all of the Democrats needs to be in DC. Some of the Democrats can tear gassed with the protestors, show solidarity, build awareness, etc by being on the ground.

To filibuster in the Senate, all you have to do is send an email saying you plan to filibuster. There's no need to be in DC to filibuster.