WASHINGTON -- In a late-night voice vote, the House passed an amendment Wednesday sponsored by Reps. Peter King (R-Seaford) and Mike Thompson (D-Calif.) to boost funding for states to conduct background checks on gun purchasers by $19.5 million to $78 million -- just days after seven people died in a stabbing and shooting rampage at a California college.

But Rep. Frank Wolf (R-Va.), the main sponsor of the $51.2 billion spending bill King's measure would amend, demanded a roll-call vote -- postponing any action until at least Thursday.

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In a letter to colleagues, King and Thompson argued that states don't have the funds to adequately check would-be gun buyers to screen out felons, domestic abusers and the seriously mentally ill. A review of five states, the letter said, found at least 2.5 million outstanding arrest warrants had not been entered into the National Instant Criminal Background Check System.

The amendment has backing from the Coalition to Stop Gun Violence, the Brady Campaign, Sandy Hook Promise, Third Way and Americans for Responsible Solutions, a group co-founded by former Rep. Gabrielle Giffords (D-Ariz.).

The National Rifle Association has not posted its position on the bill, but has opposed similar measures in the past. Its view would have sway in the Republican-controlled House.

The amendment would shift money from other areas in the $51.2 billion House appropriations bill for the departments of Commerce and Justice, among other agencies, for the fiscal year beginning Oct. 1.