Generally, the more time and trouble something takes to do, the more seriously people take it. Conversely, the easier it is to forge something the less seriously it's taken. There are a lot of things you can do when you want to get a message across to elected officials that are far more effective than e-petitions. In rough order of effectiveness:
Speak with your elected officials in person. This most direct and effective method of advocacy is often overlooked because it seems difficult. Members of Congress have offices in their congressional districts. You don't have to be a VIP to get into the office for a meeting, you just have to call ahead for an appointment. Don't be intimidated -- they work for you! You can find tips for such meetings at the ACLU's website.
Telephone your representatives to express your views. You don't have to be eloquent -- if it's an issue receiving a lot of attention, staffers will simply log that you called on the 'pro' or 'con' side of the question.
Hand-write or type a letter to your elected representatives. Since these can't be mass-produced by a lobbying group, they are typically taken VERY seriously. Have a letter-writing party at your home or at a table at school, work, or church with sample letters folks can imitate if you want to encourage others to help. Use your own words, sign it, and mail it to your representatives. When it's sent by regular postal mail, representatives are more confident that the letter came from within their district.
If you are not comfortable with your own writing skills, print out a sample letter from an organization that feels as you do (e.g., Amnesty International, the Human Rights Campaign, the ACLU, etc.), sign it by hand, and send it by regular postal mail. The words may not be your own, but your representative will be more confident that the sentiment really came from a constituent instead of a special interest.
Start a hard-copy petition. Contact the party you're trying to influence and find out what type of petition and response might sway their opinion or be considered valid under law. Make sure that you ask for signatures from voters registered within the district of the person to whom you're sending the petition. Have printed (legible) names and addresses along with signatures, so the representative knows that the petition is supported by voters in her/his constituency.
Editor's Note: The problem with Armchair Activism is that we're much more likely to take a political stand on an issue if it's easy to do and we won't lose anything in the process. Sometimes, when something is so easy to do, we feel guilty about not doing it - even though we know in our hearts, that the effort is futile. Few things worth doing are ever easy. E-mail can be a powerful tool for coordinating a campaign, but it should not be the campaign.
To find contact information (address, phone, e-mail) for your congressmen, look them up on the House of Representatives and Senate websites.