In his national address last night, President Obama said, “The American people may have voted for divided government, but they didn’t vote for a dysfunctional government. So I’m asking you all to make your voice heard. If you want a balanced approach to reducing the deficit, let your member of Congress know. If you believe we can solve this problem through compromise, send that message.”

I guess I’m jaded, because I didn’t really expect large numbers of Americans to respond to the presidential call to action. I’m glad I was wrong — a lot of people are taking the president’s advice.

Tuesday morning, the congressional switchboard sent an email to congressional offices that read: “Due to the high volume of external calls, House telephone circuits serving 202-225-XXXX phone numbers are near capacity resulting in outside callers occasionally getting busy signals.” The 225 exchange is the one used by members of the House. In spot calls to six House offices Tuesday morning, a busy signal was often found.

And that’s just the phone lines. House web servers have also been overwhelmed.

Obviously, there’s no way to know for sure what those reaching out to lawmakers are saying, or what the ratio is of pro-compromise folks to anti-compromise. That said, if the calls are roughly equivalent to all the recent national polls, most of those contacting the Hill agree with the White House, not congressional Republicans.

What’s more, the volume is likely to increase — Organizing for America will reportedly use its lists today to encourage more outreach, nearly all of which will likely be in opposition to the GOP.

Following up on an earlier point, it’s safe to assume that most of the hard-line conservatives are immune to public pressure, and won’t care about any of this. But for GOP members who are on the fence, and are perhaps worried about their re-election prospects in competitive districts, could a sudden flood of calls, letters, emails, and faxes move a few House votes? Absolutely.

If you’ve been trying to reach Capitol Hill to weigh in with your own concerns, you can keep trying the main switchboard; you can contact your representative’s local offices, and there are some online tools to help people contact Congress that still appear to be working.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.