Although the mainstream organized tea party or more importantly the tea party organizers claimed to be opposed to the bailouts they waited until after the national elections to publicly state strong opposition.
The federal government had to become involved in the collapse - with around 16 trillion in federal state local and individual retirement funds at risk and unknowns like 30 - 70 trillion in unsecured derivatives like credit default swaps the federal government had little choice realistically but to get involved or probably end up refinancing the entire US economy after an almost certain collapse.
There were protests to the bailouts before the election. A small group of right leaning libertarian outsiders/Ron Paul followers early on, were vocally against the bailouts. Ironically the right fringe outside the tent and these leftists are the probably the legitimate populist roots (and here) for the Tea Party's expressed anger.
That was hijacked by the current astroturfed group that claimed to oppose government intervention yet failed to show any organized resistance and no good argument to the bailouts until a new president was inaugurated. Since then no particular rule other than extreme dissonance seems to characterize their views.
The only real serious resistance to bailout initiatives that came from any part of the organized right that I know of was in the form of a lawsuit from the Thomas More Law Center (a right wing issue litigation mill) to challenge the Emergency Economic Stabilization Act of 2008, ludicrously claiming that it unconstitutionally promotes Islamic law (Sharia) and that religion. The lawsuit was filed because AIG provides Takaful Insurance Plans, which, according to the company, avoid investments and transactions that are "un-Islamic."
Regardless, the bottom line is before Bush left office the implications of this near collapse were known and being legislated for even if the current Tea Party "patriots" made no effort then or in the last eight years to make their voices known.
Indeed before Bush left power the following was enacted:
Emergency Economic Stabilization Act of 2008 October 3, 2008 "The Bailout" authorized the United States Secretary of the Treasury to spend up to US$700 billion and create the Troubled Assets Relief Program.
Troubled Asset Relief Program Originally expected to cost the U.S. taxpayers as much as $300 billion now (CBO) estimated the total cost would be $25 billion.
Economic Stimulus Act of 2008 signed into law on February 13, 2008 by President Bush
But these were not the only costly programs enacted by president Bush and combined with recovery efforts make up the lions share of the US deficit :
Recently, in at least the seventh raising of the debt limit in the last decade, despite being warned of the effects of near default, the far right republicans i.e. the tea party claimed "debt fear" was preventing growth and obstructed the raising of the ceiling. This led directly to a downgrade and a week of great instability in world markets. Leaders of the tea party have since blamed "deficit fear" but the fact remains that throughout the stock market drops recently US debt was the one safety people invested heavily in.
So again the exclusive public focus on the new administration is problematic.
In conclusion; the Tea Party has different factions and varying origins sometimes at philosophical odds with one another, the concepts that seem to be all uniting are; a anti environmental, anti intellectualism and a anti liberal social/social expenditure philosophy.