Early 2009 was a mess. The deficit in 2008 was around $400-450 billion, but $200+ billion of that was an anti-recession stimulus package; some wanted it larger, but many, including then-Senator Obama, argued that the deficit was too large and had to be brought under control. Notice that the recession was all but reported on by then--leading indicators said "recession" and economic activity was already reported as depressed. If the recession hadn't hit, there's a good chance that 2009 would have had a deficit in the double digits. It had been trending downward for years, and with the withdrawal from Iraq already inked, signed, and ratified before Obama took office that expense would have faded.
By 1/20/09 one half of TARP had been released by Congress. The other half wasn't requested by Bush II and wouldn't be unless Obama himself personally requested it. It was requested, Pelosi verified this, and so a day or two before inauguration $350 billion in money was authorized for disbursement. No time for Bush II to do squat with it--he hadn't fully disbursed the first tranche. The disbursement largely turned out to be loans that were mostly repaid in the next few years--is this a true deficit or an accounting deficit? Other portions of TARP was for stuff like GM stock, much of which has been sold and the money returned to the Treasury as "income," even though it's not "true income" in any normal sense of the word for most people. The government has "expense" and "income"--not "loan" or "investment".
There was a $400 billion + spending bill held up in Congress in 01/09. It was higher than Bush II's budget called for. Bush was going to veto it if it was passed. Congress refused to amend it to make it something he'd sign. So Congress sat on it for months--better to have no bill than a vetoed bill. It was quickly passed and signed into law after the inauguration. Is that Bush II spending or Obama spending? It became part of the baseline spending for those agencies.
There was the second stimulus, the "Obama" stimulus. It's nominally in that last "Bush budget year" but was formulated, passed, and signed over a month after inauguration. Was that Bush II deficit spending or not? (If so, then it's actually the Bush stimulus that so many think saved the economy, which I think would rankle people--as it should.)
And how do you handle a deficit that's increased because of spending and a deficit that's increased because of reduced revenues because incomes have fallen?
Yours is the kind of questions that requires so many assumptions be made explicit for it to have any possible answer that's isn't mostly faith-based or made up out of whole cloth.