The House has every right to shut the government down. "No money shall be drawn from the treasury, but in consequence of appropriations made by law..."Every person alive in this country, except for conservative extremists and morons , KNOW that the Republicans are responsible for this shutdown, just like the only other one in this country's history, initiated by then Speaker of the House Newt Gingrich. So, it really doesn't matter that the Republicans say they aren't the cause this time, again, because the majority of voters in this country do. I just hope the they pay for their stupidity in 2016.
Of course, your claim that there's only been one other shutdown is an ignorant one since there have now been 18 shutdowns. 5 occurred in entirely Democrat-controlled governments; 7 occurred with the same situation we have now, which is one party with the presidency and senate and the other party with the house; 2 occurred with a Republican president and Democrat senate/house control. Democrats have shut the government down 14 times while Republicans have only done it 4 times. So in reality, you might say that Republicans got this tactic from Democrats, who used it against them 9 times and also 5 times against a president from their own party.
The midterm is probably not going to be good for Obama. Historically they aren't; all of the enthusiasm behind him--which brought a lot of Democrat senators from Republican states into office in 2008--has now eroded; the Democrats' fundraising capability got wrapped up in Obama's campaign organization such that the Democratic National Committee has a huge pile of debt and is now teetering on bankruptcy; and Republicans are more likely to turn out since there will be no presidential race and anti-Obamacare sentiment will be very high. I already suggested that this stunt is meant to appeal to Republican midterm voters, who are more likely to vote in 2014 than Democrats will be.