The website DownForEveryoneOrJustMe.com confirms that the following websites were among those affected:
-Senate Minority Leader Mitch McConnell (R-Ky.)
-House Speaker John Boehner (R-Ohio)
-Rep. Elliot Engel (D-N.Y.)
-Sen. Mike Crapo (R-Idaho)
-Sen. Jim DeMint (R-S.C.)
-Rep. Charles Rangel (D-N.Y.)
-Sen. Rand Paul (R-Ky.)
-Sen. Amy Klobuchar (D-Minn.)
-Sen. Tom Harkin (D-Iowa)
Not all are down though. Among the congressional websites that currently work without any problems is Senate Majority Leader Harry Reid's (D-Nev.). The websites of House Minority Leader Nancy Pelosi, Rep. Jarry Nadler (D-N.Y.) and Rep. Ed Markey (D-Mass.) also work.
The cause of the outages is not yet clear, though Obama did encourage people to contact their representatives in Congress.
UPDATE (10:53 p.m. ET): Some of the sites above are now experiencing intermittent issues. They seem to return briefly and go back down. Some say "Server too busy," others say "Server error," and some do not load at all.
UPDATE (11:10 p.m. ET): All the above sites seem to be back now except for Boehner's, however most are loading slowly.
UPDATE (11:25 p.m. ET): Also down at this time are the sites of Rep. Rick Crawford (R-Ark.), Rep. Mike Ross (D-Ark.), Rep. Steve Womack (R-Ark.), Sen. Mark Pryor (D-Ark.) and Sen. John Boozman (R-Ark.).
UPDATE (1:50 a.m. ET): The House and Senate websites now seem back to normal.