Yes, all spending bills must start in the house so of course the budget must originate there, after the President sends his budget for consideration. Unfortunately, we haven't had a budget passed in something like 840 days now and have been operating under a continuing resolution until the end of FY2011 which was most recently presented and passed with minor spending cuts. As I understand it, the only reason the government wasn't shut down was the bill to make sure our military still got paid was not passed by the Senate. This is the same military the Senate is holding hostage now, along with the threat of default, Social Security and Medicare.
The reason our credit rating is in danger isn't necessarily the threat of default, but is that we have spent close to 9 trillion in the last 2.5 years and can't find cuts 1/3 that amount over 10 years because the senate and president refuse to even consider any bills that don't raise taxes on those who earn 250k or more a year.
I appreciate that we are a republic and not a democracy, plutocracy or monarchy. Presidents have limited power, and still get credit or blame for what happens during their administration, even if they didn't cause it. Fair or not, it's the way it is.
Your arguments on the Constitution are not without merit, and I don't believe that the President is authorized under the Constitution to make such an increase. It's been nice to have a well reasoned discussion with someone who has opposing views, without things turning ugly.