As President Barack Obama starts his second term, the bond market is already telling him that the administration's forecasts for economic growth over the next four years are too optimistic.

The Office of Management and Budget predicts yields on 10-year Treasury notes will rise to average 4.1 percent in 2015 and 4.9 percent in 2017 as the economy expands at about a 4 percent rate in the second half of Obama's term. Bond prices suggest the yield, now at about 2 percent, will average below 3 percent two years from now, implying that gross domestic product will fall short of OMB projections, according to data compiled by Bloomberg.

While Obama's legacy may depend on a recovering economy, the bond market is signaling GDP may not in the next few years exceed the 3.3 percent annual average of the decade preceding the financial crisis and tax revenues will fall short of what the president needs to close the budget gap. That's not all bad news because Treasury borrowing costs just above last year's record lows mean easy credit for consumers and companies as well as sustained demand for riskier assets such as stocks.