Senate Vote Kills Gun Safety Bill--Did they Vote their People's Wishes?

The Senate just voted down a proposal to create a system of universal background checks on gun purchases, thus closing the so-called "gun show loophole" and "straw purchases." On an issue where 85-90% of the public supports such a bill, did those senators vote the wishes of the people they were elected to support? The vote was highly partisan--in a 54-46 vote, 4 Democrats voted against the bill, while 39 Republicans voted against it. Those senators are listed below, by state.

Some have argued that while the high support for background checks represent national majorities, they do not represent the states from where these senators come. However, that is simply not the case--the high support for background checks has held across states, in those polls that list results by state. For example, this recent poll shows that even in states that went for Romney in the last election, there is still high support for background checks. Republican senators in those states still voted against the bill.

Senator	State	Population supporting background checks for gun purchases
Alexander	TN	No data
Ayotte	NH	89%
Barrasso	WY	No data
Baucus	MT	79%
Begich	AK	90%
Blunt	MO	85%
Boozman	AR	84%
Burr	NC	90%
Chambliss	GA	91%
Coats	IN	89%
Coburn	OK	87%
Cochran	MS	No data
Corker	TN	No data
Cornyn	TX	No data
Crapo	ID	No data
Cruz	TX	No data
Enzi	WY	No data
Fischer	NE	No data
Flake	AZ	90%
Graham	SC	No data
Grassley	IA	88%
Hatch	UT	83%
Heitkamp	ND	94%
Heller	NV	86%
Hoeven	ND	94%
Inhofe	OK	87%
Isakson	GA	91%
Johanns	NE	No data
Johnson	WI	No data
Lee	UT	83%
McConnell	KY	82%
Moran	KS	No data
Murkowski	AK	60%
Paul	KY	82%
Portman	OH	83%
Pryor	AR	84%
Reid	NV	86%
Risch	ID	No data
Roberts	KS	No data
Rubio	FL	91%
Scott	SC	No data
Sessions	AL	No data
Shelby	AL	No data
Thune	SD	No data
Vitter	LA	85%
Wicker	MS	No data