Not exactly. The sources they cite say this:
All the sources also mention the potential problems due to the stimulus, but the fact remains that spending growth under Obama has been quite low.
You can make other claims, if you like; there are plenty of potential ones (such as "Obama would've spent more if Congress hadn't stopped him." Note that "but the stimulus made baseline spending much higher" isn't actually that good--even if we measure from FY 2008, spending increases only amount to 5%). With this particular one, the facts are on Obama's side.
Why in the world is the WaPo "fact checking" article (LOL) starting with fiscal year 2008?
Fiscal year 2008 = October 2007 - September 2008
Fiscal year 2009 = October 2008 - September 2009
Fiscal year 2010 = October 2009 - September 2010
Obama didn't come into office until nearly a third of the way through fiscal year 2009, and the fiscal year 2010 budget, submitted to congress by Obama during his 2nd or 3rd week in office (early February 2009), was actually made by the Bush administration and handed off to the Obama administration for submission, as is the case with every new president's first budget.
The budgets the Obama administration would be responsible for drafting are Fiscal Years 2011, 2012, 2013, and 2014 for his first term. 2015, 2016, 2017, and 2018 for his second term if re-elected. Though he will not submit the 2018 budget, because that will be submitted in February of 2017, a few weeks after Obama's 2nd term would end.