(CNN) The mass shooting at the baseball practice targeting Republican lawmakers has rattled Capitol Hill, and comes on the heels of an uptick in threats coming into members' offices.

There is bipartisan agreement that procedures need to be adjusted to keep members safe in potentially dangerous situations, but there's no consensus yet on whether more taxpayer money should be spent to protect members of Congress.

"If I was the speaker, if I was in charge, I'd do it tomorrow. I'd do a stand-alone bill about members' safety or change a rule, to make sure the 435 members who take this oath to the Constitution to take this job are safe and their families are safe," Rep. Cedric Richmond, a Louisiana Democrat who serves as Chairman of the Congressional Black Caucus, told reporters Thursday. He said he believes the cost would be roughly $1 million, and "well worth it."

Even before the shooting there were discussions among leaders about new security needs for lawmakers. House Speaker Paul Ryan met with House Minority Leader Nancy Pelosi last week to discuss protocols and rules, according to Ryan's spokeswoman. Richmond met recently with Ryan to relay concerns from fellow CBC members about threats they received in recent months and to press for more resources.

"I've had threats, and most members I know have had threats," the Louisiana Democrat said.

New York Republican Rep. Claudia Tenney told CNN that she has had numerous phone and email messages warning that people wanted to harm not only her, but her son, who serves in the military in Iraq. Just hours after the shooting, her office received a message from someone referring to Scalise being targeted that said "one down, 216 to go."

"We've got to look at the rules," House Majority Leader Kevin McCarthy told reporters, noting that he and others have been working through questions about whether it's appropriate to have members use their taxpayer funded "MRA" which stands for "Member's Representational Allowance" for security costs. There would need to be a new rule issued if members wanted to use any of those funds for home security costs.

Currently lawmakers can only use money from campaign accounts to cover security if they have had threats posed against them. According to senior House aides, the House Sergeant at Arms, Paul Irving, is discussing with the Federal Election Commission about providing new guidance giving members permission to shift some of their campaign funds for security if the threat is determined to be serious enough.

North Carolina Rep. Mark Meadows, who chairs the conservative House Freedom Caucus, didn't see the need to boost members' personal office budgets, saying, "I have a bigger problem with my staff not getting paid enough than with the money for security."

But Pelosi told reporters Thursday that while she trusts the Capitol Police to design security procedures, "I do think and I would support, and I have suggested they need a bigger budget."

Irving, who oversees the Capitol Police, briefed House Republicans Thursday morning on efforts by law enforcement to examine how to handle new threats, and potentially make changes to how they handle events like baseball practices with large groups of members.

"It gets back to budgets and I understand that, and what is a threat and what is not a threat. But when the threat comes to you personally it's a threat," Texas GOP Rep. Roger Williams told reporters. Williams injured his leg diving into the dugout at the baseball field when the shooter opened fire, and an aide from his office was also injured.

Another GOP member on the team who escaped the gunfire, Rep. Barry Loudermilk of Georgia, noted that rank-and-file members don't have protection assigned to them so they are on their own. "We also need to look at security detail. If Scalise hadn't been on our team, it would have been really bad. At what point do you have a congregation of members -- and we're not even more special than anybody else, but we are targets -- do you have a security detail with you?"

Richmond said Ryan was "very receptive" to his push for additional resources. But he also admitted that it would not have stopped the incident at the baseball field in Alexandria, Virginia.

The issue of an increase for security costs could be inserted into the upcoming debate on annual spending bills. Richmond didn't rule out introducing legislation if needed, and members said the talks about the issue will certainly ramp up in the wake of the violent attack on the GOP baseball team.

Multiple members, including Tenney, told CNN they rely on local law enforcement in their districts to protect them at parades, town halls and public appearances when they are not on the Capitol Hill campus, and most volunteer to send officers.

"We just make the phone call and they provide the protection that's part of what they do just being servants of the community," Meadows said, noting that after the shooting both Democratic and Republican sheriffs told his office they would help secure his events as needed.

Georgia GOP Sen. David Perdue said it was unrealistic to provide security for every member of Congress. "You can't do it. But I think if you have more than a few senators and representatives getting together in a group, there ought to be some kind of security there. I don't think you want to build a barrier between individuals and their constituents or individuals and the public. That's not America. So, it's one of the risks you take on."

McCarthy said discussions will continue to respond to increased anxiety among members.

"We want to make sure people are secure, and people feel secure in the process."