The Washington senator launched the online tool less than a week after she confirmed that Democrats would move a budget through her committee. Senate Democrats last passed a budget in April 2009.
In launching MyBudget, Murray talked about raising further revenues, a topic that Republicans say they have no interest in, and strengthening programs like Medicare.
House Republicans have said they will produce a budget that balances in a decade, which is quicker than the last two efforts from Ryan and will likely require deeper cuts.
The House also passed a measure last week that tied a short-term measure to push back the fight over the debt ceiling with a proposal to withhold lawmaker pay if the House or Senate fail to pass a budget.