The senators convened to vote on procedures for ex-president Trump's impeachment. Some forty Republicans think that there was indeed some fraud in the election. Most of them are from red states and were safely re-elected. "But there could be fraud anywhere, I could have won a few percent more if there were no mail-in-ballots," said senator Bill Clarkson from Kansas.
The thinking goes like this: They could have won by bigger margins, all of them, but Trump was losing in battle-ground states by such small margins that the mail-in-ballots and so called "cured" ballots made a difference. These were ballots where the election official marked the ballot to be fixed and the voter then came and put in the missing information on the outer envelope and the ballot went on to be counted. But days later from other ballots in that area.
Going along with this thinking the demonstrations and the insurrection at the Capitol were justified. Therefore Trump was just reacting along with the public, his supporters.
Of course, the objection to counting the electoral votes did not carry either the house or senate. It would have been necessary to reject the electors in both houses. "But that's beside the point," claims Senator Clarkson. "The voices must be heard, so that we can pass laws to make elections more secure."
What these laws might be is anybody's guess. The federal government does not oversee elections, the states do. If some human rights violations, Jim Crow laws etc. were in place, that would be another matter. But the Voting Rights Act of 1965 has been trashed by the Supreme Court, and no longer applies. Because we no longer have any racism, they say.